Publications of Carl H. Gibson, with notes.
1.  Gibson, C. H. and W. H. Schwarz, "Detection of 
Conductivity Fluctuations in a Turbulent Flow Field,"  J. 
Fluid Mech. 16: 3 (1963), 357-364 (8 pages).
This paper describes a new technique for measuring 
turbulent temperature and salinity with very high spatial 
resolution and essentially infinite frequency response using a 
"single electrode probe", where one electrode is very much 
smaller than the second.  The method has been widely 
adopted in laboratory studies, and is the standard device 
used by Russian scientists to detect conductivity (usually 
temperature) microstructure from dropsondes and high speed 
towed bodies.  The probe was essential in demonstrating the 
validity of the Batchelor (1959) turbulent mixing theory for 
the first time in the following paper.

2.  Gibson, C. H. and W. H. Schwarz, "The Universal 
Equilibrium Spectra of Turbulent Velocity and Scalar 
Fields,"  J. Fluid Mech. 16: 3 (1963), 365-384 (20 pages).
This was the first attempt by anyone to test the Kolmogorov 
(1941) universal similarity hypotheses using spectral 
measurements from wind tunnels (Stewart and Townsend), 
a water tunnel (my thesis work at Stanford), and the ocean 
(the data of Grant, Stewart and Moilliet from tidal channels 
and submarines that collapsed beautifully on the 
Kolmogorov scaled laboratory data I had already finished 
and plotted-producing a true believer).  This was also the 
first laboratory test of the Batchelor high Prandtl number 
turbulent mixing theory, demonstration of the scalar inertial 
(k-5/3) and viscous convective (k-1) subranges, and 
extraction of the universal constants for these scalar 
subranges as well as the velocity universal inertial (k-5/3) 
subrange constant.  

3a.  Priestly, M. B. and C. H. Gibson, "Estimation of 
Power Spectra by a Wave-Analyzer," Technometrics 7: 4 
(1965), 553-559 (7 pages).
This was before tape recorders, digitizers, the fast fourier 
transform, or any of the present day luxuries.  The paper 
describes how to measure spectra from a stationary time 
series using a tunable filter and analog averager.

3b.  Letter to the Editor on "Estimation of Power Spectra by 
a Wave-Analyzer," Technometrics 8 (1966), 562-568 (7 
Somebody didn't understand and we had to explain it again.

4.  Gibson, C. H., C. C. Chen and S. C. Lin, 
"Measurements of Turbulent Velocity and Temperature 
Fluctuations in the Wake of a Sphere," AIAA J. 6: 4 (1968), 
642-649 (8 pages).
Using much better hot film anemometer equipment, a 
stainless steel water tunnel, higher resolution 
microconductivity probes, instrumentation grade analog tape 
recorder, a proper digitizer, and digital data analysis methods 
it was possible to confirm the universal spectral forms of the 
Kolmogorov (1941) and Batchelor (1959) turbulence and 
turbulent mixing theories published in ref. 2, and also 
determine the c budget for turbulent wakes.  This experiment 
clearly showed me the fallacy of the "well known" 
turbulence cascade direction from large scales to small.  
Turbulence always starts by eddies forming at the 
Kolmogorov (viscous) scale and cascades to larger scales by 
a sequence of eddy pairings, with entrainment of the 
irrotational (nonturbulent) external fluid at the Kolmogorov 
(viscous) scale.  Everyone will tell you the opposite.  Don't 
believe them.

5.  Gibson, C. H., "Fine Structure of Scalar Fields Mixed 
by Turbulence: I.  Zero-Gradient Points and Minimal 
Gradient Surfaces," Phys. Fluids 11: 11 (1968), 2305-2315 
(11 pages).
I realized a couple of years after my thesis was published 
that the physical rate-of-strain (g) mixing mechanism behind 
the Batchelor (1959) mathematical theory could be extended 
to strongly diffusive (low Prandtl number) scalar fields 
mixed by turbulence.  I showed that scalar structures with 
zero and minimal gradient move with the fluid and are 
therefore subject to local straining, even if their radii of 
curvature are much larger that the scales of uniform 
straining, contrary to the Batchelor, Howells, and Townsend 
(1959) theory that assumes g is irrelevant for Pr  1.  After 
three years of cordial correspondence with George Batchelor 
about my theory, I finally gave up and published in Physics 
of Fluids.  I was able to extract a bet from George that if my 
theory were true I could not only have the subscription to the 
Journal of Fluid Mechanics I wanted, "but all the issues back 
to 1956".  My education would be satisfaction enough if I 
lost.  The jury is out.

6.  Gibson, C. H., "Fine Structure of Scalar Fields Mixed 
by Turbulence: II.  Spectral Theory,"  Phys. Fluids 11: 11 
(1968), 2316-2327 (12 pages).
Here the idea in ref. 5 is expressed as a universal similarity 
hypothesis similar to those of Kolmogorov (1941) for 
turbulent velocity fields, and a new "inertial diffusive" 
subrange (k-3) is predicted.  This subrange and other 
predictions of the theory were confirmed by measurements 
in turbulent mercury by my student John Clay, and 
numerical experiments with W. Ashurst and A. Kerstein in 
ref. 52 (twenty years later in JFM).
7.  Gibson, C. H. and R. B. Williams, "Turbulence 
Structure in the Atmospheric Boundary Layer over the Open 
Ocean," AGARDograph CP 48, No  5, Munich (1969), 
110-121 (12 pages).
These are the first such ocean air turbulence measurements 
ever, from FLIP with Bruce Williams of MPL, who helped 
me get started using digital techniques to study turbulence in 
and over the ocean.  We made the first underwater 
measurements I had ever seen on this unfunded cruise using 
my laboratory instruments, and I made the wise career 
decision to focus on atmospheric measurements until I was 
awarded tenure (the turbulence signals on the hot film 
anemometer were exceedingly rare and tiny in amplitude-
much too risky for an Assistant Professor to publish).

8.  Gibson, C. H., R. R. Lyon and I. Hirschsohn, 
"Reaction Product Fluctuations in a Sphere Wake," AIAA J. 
8: 10 (1970), 1859-1863 (5 pages).
Using weak acid and weak base that are non-conductors, the 
reaction product distribution is revealed by 
microconductivity probe measurements.  As far as I know, 
these measurements were (and are) unique.  The distribution 
appears just like that of a passive scalar, and since the 
product appears at scales even smaller than the Batchelor 
scale this is further demonstration of the true direction of the 
turbulence and turbulent mixing cascade (i.e.: from small to 
large scales).

9.  Gibson, C. H., G. R. Stegen and R. B. Williams, 
"Statistics of the Fine Structure of Turbulent Velocity and 
Temperature Fields at High Reynolds Number," J. Fluid 
Mech. 41 (1970), 153-167 (15 pages).
Some initial results of atmospheric measurements over the 
open ocean from FLIP.  The apparent departures of the 
universal temperature spectrum constants from the laboratory 
values at these high Reynolds numbers were subsequently 
found to be due to humidity sensitivity of the cold wires 
from salt spray contamination (part of the famous "cold 
spike" phenomenon-announced in a news conference by 
Bob Stewart and Steve Pond after the 1969 BOMEX 
expedition on FLIP near Barbados).

10.  Gibson, C. H., G. R. Stegen and S. McConnell, 
"Measurements of the Universal Constant in Kolmogoroff's 
Third Hypothesis for High Reynolds Number Turbulence," 
Phys. Fluids 13: 10 (1970), 2448-2451 (4 pages).
This is the first paper published in the western literature on 
the third universal similarity hypothesis of Kolmogorov 
(1962) on lognormality and intermittency of very high 
Reynolds number turbulence.  The hypothesis that viscous 
dissipation rate e should be lognormal was confirmed and 
the value of the constant m in his hypothesis s2lner = m ln 
(L/r) was found to be 0.4-0.5 from the spectrum of the 
dissipation which should be ~ k-1+m, where s2 is the 
variance, L is the largest eddy size of the cascade, and r is 
the averaging scale.  The paper was written in four pages in 
honor of Kolmogorov's style.  The constant is crucial to 
understanding the observed intermittency of ocean mixing, 
and is currently being rather fiercely debated by several 
prominent authors that claim m = 0.2 or less.  See ref. 68, 
77, C29, and C31 which confirm m = 0.4-0.5.

11.  Friehe, C. A., C. W. Van Atta and C. H. Gibson, "Jet 
Turbulence: Dissipation Rate Measurements and 
Correlations," AGARDograph CP 93, No. 18, London 
(1971), 88-103 (16 pages).
From measurements Carl Friehe and John La Rue (now 
Professors at UCI) made in the UCSD gymnasium from a 
huge jet, and a literature search, we discovered a very useful 
correlation equation for the viscous dissipation rate in jets [e 
= 48 (U3/D) (x/D)-4].

12.  Gibson, C. H. and P. J. Masiello, "Observations of the 
Variability of Dissipation Rates of Turbulent Velocity and 
Temperature Fields," in Lecture Notes in Physics,  Vol. 12, 
Springer-Verlag (1972), 427-448 (22 pages).
Several aspects of the Kolmogorov (1962) third universal 
similarity hypothesis for high Reynolds number turbulence 
were tested using hot wire turbulence measurements 30 m 
over the ocean from FLIP during BOMEX and off the coast 
of Mexico, and from temperature and velocity measurements 
in a Re = 120,000 jet in the UCSD gymnasium.  The 
universal intermittency constant m was found to be in the 
range 0.4-0.5 by several methods, including a direct test of 
s2lner = m ln (L/r) for various averaging scales r.  It was 
discovered that the use of adequate high pass filter setting are 
crucially important, since the universal dissipation subrange 
extends to much smaller scales (by a factor of 7) than that of 
the turbulent velocity (see ref. C31).  The Gurvich-Yoglom 
cascade model of lognormality was tested and found to be 
generally valid (independent identically distributed 
dissipation ratios were found over a wide range of scales) 
but their assumption that all squared quantities are lognormal 
failed for the small value range.

13.  Gibson, C. H. and P. A. Libby, "On Turbulent Flows 
with Fast Chemical Reactions: Part II.  The Distribution of 
Reactants and Products Near a Reacting Surface," Combust. 
Sci. Technol. 6 (1972), 29-35 (7 pages).
Using the smallest microconductivity probe I ever succeeded 
in making (tip size 1/4 micron from an electron microscope 
photograph) it was possible to detect the very thin reaction 
product zone for the fast weak acid (acetic) weak base 
(ammonium hydroxide) reaction, and compare with a 
reacting boundary layer theory of Professor Libby.

14.  Stegen, G. R., C. H. Gibson and C. A. Friehe,  
"Measurements of Momentum and Sensible Heat Fluxes 
over the Open Ocean,"  J. Phys. Oceanogr. 3: 1 (1973), 86-
92 (7 pages).
Basic heat, mass and momentum flux coefficients measured 
directly from FLIP, very carefully by Stegen and Friehe 
during their post doc days with me.

15.  Gibson, C. H. and R. B. Williams, "Measurements of 
Turbulence and Turbulent Mixing in the Pacific Equatorial 
Undercurrent," in Oceanography of the South Pacific 1972 
(Proceedings of the International Symposium on 
Oceanography of the South Pacific), R. Fraser (Ed.), New 
Zealand Commission for UNESCO, Wellington (1973), 19-
23 (5 pages).
This is the first report from an unfunded pickup cruise in 
April, 1971, to measure turbulence in the Cromwell current 
with all the instruments I could scrounge from my water 
tunnel laboratory.  We put a fast ducted current meter and a 
quartz fiber cold film on an 800 lb lead weighted fish, and 
towed for two weeks at hard labor before we found any 
recognizable turbulence.  Now I realize that equatorial 
turbulence is probably the most difficult turbulence to detect 
in the ocean because it has maximum intermittency factors 
s2lner, from the s2lner = m ln (L/r) third hypothesis 
equation since the lack of Coriolis forces allows L to 
increase without bound.  Intermittency factors can be in the 
range 6-7, giving mean to mode ratios over 104 for the pdfs 
of e and c.  Mean values are completely dominated by a few 
powerful patches, and we were lucky to find any even with 
this much towing.

16.  Gibson, C. H., "Digital Techniques in Turbulence 
Research, "AGARDograph AG 174 (1973), 26pp (26 
We made the first direct digital data acquisition and spectral 
analysis ever for ocean turbulence during the 1971 equatorial 
undercurrent cruise.  This report describes some of the 
techniques developed later in the laboratory and at sea 

17.  Gibson, C. H., L. A. Vega and R. B. Williams, 
"Turbulent Diffusion of Heat and Momentum in the Ocean, 
"Adv. Geophys. 18A (1974), 353-370 (18 pages).
Some unexpected results of near surface turbulence 
measurements over waves.  Rather than maximum 
dissipation rates in the lee of wave crests the maximum was 
found upwind (the waves were moving faster than the 
18.  Williams, R. B. and C. H. Gibson,  "Direct 
Measurements of Turbulence in the Pacific Equatorial 
Undercurrent," J. Phys. Oceanogr. 4: 1 (1974), 104-108 (5 
Bruce Williams' thesis work, showing his most active towed 
body data had e values up to 0.1 cm2 s-3 and c values up to 
10-4 C2 s-1 at the core depth of the Cromwell current at 
the equator and at 1 N from many days of towing.  These 
values were the first ever measured in the Pacific Equatorial 
Undercurrent, and were 20 years ahead of their time.  They 
have been furiously denied as impossible over the years by 
the oceanographic microstructure community on the grounds 
that these dissipation rates are about 104 times larger than 
anything seen by other investigators (except the Russians 
who found the same result in the Limonosov current, also 
from towed bodies).  However, during the second Tropic 
Heat expedition when many thousands of dropsondes 
through the core were carried out-the number needed to 
encounter one dominant turbulence patch at this depth of 
maximum lognormal dissipation rate with maximum 
intermittency-one such patch was finally detected (many 
fossils of previously turbulent patches were found).  

19.  Schedvin, J. C., G. R. Stegen and C. H. Gibson,  
"Universal Similarity at High Grid Reynolds Numbers," J. 
Fluid Mech. 65 (1974), 561-579 (18 pages).
By an interation scheme it was possible to show that the 
anomalously large value of the Kolmogorov inertial 
subrange constant reported by Kistler and Vrebolovich for a 
very high Reynolds number grid turbulence flow was almost 
certainly due to the wire length correction.

20.  LaRue, J. C., T. K. Deaton and C. H. Gibson, 
"Measurement of High Frequency Turbulent Temperature," 
Rev. Sci. Instrum. 46: 6 (1975), 757-764 (8 pages).
Circuitry was developed to permit high frequency 
measurements from the SIO DC3 aircraft in conjunction with 
FLIP measurements.

21.  Gibson, C. H., Osmidov, R. V. and V. T. Paka, 
"Soviet-American Oceanic Turbulence Intercomparison 
Experiment on 11th Cruise of the DMITRI-MENDELEEV," 
Akad. Nauk USSR Oceanology XV (1975), 191-194 (4 
During a visit to Moscow for an IUTAM meeting, it was 
possible to meet Professor Osmidov at the Shirshov Institute 
of Oceanology.  We discovered we were both measuring 
turbulence in the equatorial undercurrent cores 
simultaneously in 1971 in different oceans, and that we both 
found approximately the same e values.  At the invitation of 
Professor Monin and the Academy of Science of the USSR, 
I was invited to take part in an intercomparison turbulence 
study on board the DMITRI-MENDELEEV in 1974.  John 
Schedvin, Tom Deaton and I joined the cruise, and analysis 
of the data constituted John Schedvin's Ph. D. thesis, which 
showed the first well documented fossil turbulence in the 

22.  Friehe, C. A., C. H. Gibson, F. H. Champagne and J. 
C. LaRue, "Turbulence Measurements in the Marine 
Boundary Layer," Atmos. Tech. 7 (1975), 15-23 (9 pages).
Heat, mass, and momentum exchange coefficients from a 
variety of settings around the world from careful 
measurements by this excellent set of my post docs, all of 
whom are now university Professors.

23.  Friehe, C. A., J. C. LaRue, F. H. Champagne, C. H. 
Gibson and C. F. Dreyer, "Effects of Temperature and 
Humidity Fluctuations on the Optical Refractive Index in the 
Marine Boundary Layer, "J. Opt. Soc. Am. 65: 12 (1975), 
1502-1511 (10 pages).
We found that different combinations of temperature and 
humidity determined by the boundary layer conditions could 
have dramatically different effects on the "seeing".  Over the 
ocean the effects of the two fields on refractive index 
typically were additive, but over the Salton Sea they 

24.  Mestayer, P. G., C. H. Gibson, M. F. Coantic and A. 
S. Patel, "Local Anisotropy in Heated and Cooled Turbulent 
Boundary Layers, "Phys. Fluids 19: 9 (1976), 1279-1287 
(9 pages).
Investigations into the ramplike structures typical of the 
temperature fluctuations over a hot or cold boundary, and the 
connection to anisotropy (nonzero skewness of the 
temperature derivative) observed in the microstructure.

25.  Gibson, C. H., C. A. Friehe and S. O. McConnell, 
"Structure of Sheared Turbulent Fields," Phys. Fluids 20: 
10, Pt. II (1977), S156-S167 (12 pages).
Further discussion of anisotropy effects, this time in the 
vertical velocity derivatives.  The effects were barely 
detectable, and not in conflict with Kolmogorov's 
assumption of an approach to local isotropy at very high 
Reynolds number.

26.  Gibson, C. H., "Detection of Oceanic Microprocesses 
by Towed Profiling Sensors," Proceedings of the 6th 
Australasian Hydraulics and Fluid Mechanics Conference 
(Sidney, Australia, December 1977), UNESCO (1980), 68-
71 (4 pages).
A review of the advantages of using towed bodies to 
measure microstructure in the ocean rather than dropsondes.

27.  Schmitt, K. F., C. A. Friehe and C. H. Gibson, 
"Humidity Sensitivity of Atmospheric Temperature Sensors 
by Salt Contamination," J. Phys. Oceanogr. 8: 1 (1978), 
151-161 (11 pages)
It took three FLIP expeditions at hard labor to pin down this 
negative effect, and finally explain the peculiar results of ref. 
9 and the "cold spikes" observed on every temperature 
sensor during BOMEX nine years earlier.

28.  Gibson, C. H., "Zero Gradient Points in Turbulent 
Mixing," in Lecture Notes in Physics, Vol. 76, Structure 
and Mechanisms of Turbulence, Pt. II, C. H. Fiedler (Ed.), 
Springer-Verlag (1978), 347-352 (6 pages).
A review of my 1968 theory and available evidence about 
low Pr turbulent mixing.

29.  Mestayer, P. G., F. H. Champagne, C. A. Friehe, J. 
C. LaRue and C. H. Gibson, "Estimation of the Fluxes over 
the Ocean by the Covariance and Dissipation Methods," in 
Turbulent Fluxes Through the Sea Surface, Wave 
Dynamics, and Prediction, Vol. 1, A. Favre and K. 
Hasselman (Eds.), Plenum Press (1978), 51-65 (15 pages).
Summary of conclusions about the relative advantages of the 
two techniques, and recommended constants.

30.  Friehe, C. A. and C. H. Gibson, "Estimates of the 
Surface Fluxes over the Ocean," in Turbulent Fluxes 
Through the Sea Surface, Wave Dynamics and Prediction, 
Vol. 1, A. Favre and K. Hasselman (Eds.), Plenum Press 
(1978), 67-79 (13 pages).
Further discussion of flux estimates over the ocean.

31.  Schmitt, K. F., C. A. Friehe and C. H. Gibson, "Sea 
Surface Stress Measurements," Boundary-Layer Meteorol. 
15 (1978), 215-228 (14 pages).
Results on the subject from Kurt Schmitt's thesis.

32.  Schmitt, K. F., C. A. Friehe and C. H. Gibson, 
"Structure of Marine Surface Layer Turbulence," J. Atmos. 
Sci. 36: 4 (1979), 602-618 (17 pages).
Results on the subject from Kurt Schmitt's thesis.

33.  Gibson, C. H., "Temperature Measurements in the 
Soviet-American Expedition to Intercalibrate Microstructure 
Measured in the Ocean," in Proceedings of the 14th Pacific 
Science Congress (Khabarovsk, USSR, August 1979), 
Akad. Nauk, USSR, Section F (1980), 130 (1 page).
A brief report of our intercalibration cruise, showing both 
sets of instruments gave the same indications of turbulence 
activity in the Flinders Current between Adelaide and 
Melbourne Australia.

34.  Gibson, C. H., "Fossil Temperature, Salinity, and 
Vorticity Turbulence in the Ocean," in Marine Turbulence, J. 
C. H. Nihoul (Ed.), Elsevier Oceanography Series, Elsevier 
Publishing Co., Amsterdam (1980), 221-257 (37 pages).
After five years of frustration trying unsuccessfully to 
publish my fossil turbulence theory and John Schedvin's 
careful PhD thesis work (422 pages) (from the 1974 
DMITRI-MENDELEEV cruise) in the refereed 
oceanographic literature (Journal of Physical Oceanography, 
Journal of Geophysical Research) I finally placed it in this 
conference proceedings book.  A typical review from JPO 
referees of this carefully written document was simply: "This 
paper is pure rubbish!".  The paper introduces the concept of 
the hydrodynamic phase diagram to classify microstructure 
as active turbulence, active-fossil turbulence, fossil 
turbulence, or non-turbulence based on a normalized Froude 
number versus normalized Reynolds number plot, and the 
semi-empirical inference that the buoyancy-inertial-viscous 
transition dissipation rate eF = 30nN2.  John was never 
allowed to publish his thesis results in the oceanographic 
literature before his untimely death.  He was the best student 
I have ever seen from SIO.

35.  Gibson, C. H., "Turbulence," in Encyclopedia of 
Physics, R. G. Lerner and G. L. Trigg (Eds.), Addison-
Wesley Publishing Co., Inc. (1980), 1072-1073 (2 pages).
Turbulence is defined, Kolmogorov's universal similarity 
theories are outlined, and the effects of stratification given.

36.  Larsen, S., J. Hojstrup and C. H. Gibson, "Fast-
Response Temperature Sensors," in Air-Sea Interaction, 
Instruments and Methods, F. Dobson, L. Hasse and R. 
Davis (Eds.), Plenum Press, New York (1980), 269-292 
(24 pages).
Discussion of measurement and frequency response 
correction techniques used in a joint study with the Danes on 
their meteorological tower in Roskilde.

37.  Gibson, C. H. and T. K. Deaton, "Hot/Cold Sensors of 
Oceanic Microstructure," in Air-Sea Interaction, Instruments 
and Methods, F.  Dobson, L. Hasse and R. Davis (Eds.), 
Plenum Press, New York (1980), 349-368 (20 pages)
Discussion of measurement strategies used in the design of 
the towed body deployed during the MILE expedition at 
ocean station PAPA.  This was the first possible 
intercomparison test of towed bodies and dropsondes in the 
same ocean region, and confirmed my opinion that 
dropsondes vastly undersample the extremely intermittent 
turbulence and turbulent mixing processes occurring in all 
ocean layers.

38.  Gibson, C. H., "Buoyancy Effects in Turbulent 
Mixing: Sampling Turbulence in the Stratified Ocean," AIAA 
J. 19 (1981), 1394-1400 (7 pages).
This paper was also unpublishable in the oceanographic 
literature for several years, so I finally sent it to a friend and 
editor of the Amer. Inst. of Aero. and Astro. J., George 
Sutton, who thought it was interesting and well written, and 
ignored his reviewers that recognized that it was 
oceanography.  It is also fluid mechanics.
39.  Gibson, C. H., "Fossil Turbulence and Internal 
Waves," in American Institute of Physics Conference 
Proceedings No 76: Nonlinear Properties of Internal Waves, 
Bruce West (Ed.), American Institute of Physics (1981), 
159-179 (21 pages).
The second successful attempt to put my fossil turbulence 
theory into print.  It slightly refines the universal constant I 
derived in ref. 34 for the inertial-buoyancy transition scale 
(Osmidov scale).

40.  Washburn, L. and C. H. Gibson, "Measurements of 
Oceanic Microstructure Using a Small Conductivity Sensor," 
J. Geophys. Res. 87: C6 (1982), 4230-4240 (11 pages).
Discusses Libe Washburn's careful analysis of the MILE 
expedition towed body measurements taken by John 
Schedvin.  Multiply redundant temperature, conductivity, 
and velocity signals are intercompared to fend off claims that 
all towed body signals are contaminated by vibration.

41.  Gibson, C. H., "Alternative Interpretations for 
Microstructure Patches in the Thermocline,"  J. Phys. 
Oceanogr. 12 (1982), 374-383 (20 pages).
The Gregg (1977) data set is compared to my fossil 
turbulence theory, and the microstructure patches presented 
are shown to be highly fossilized in all cases.  Temperature 
overturns of up to ten meters in the vertical were presented, 
with maximum possible overturns in the vertical due to 
turbulence (Osmidov scales) of only a few centimeters. 

42.  Gibson, C. H., "On the Scaling of Vertical Temperature 
Gradient Spectra," J. Geophys. Res. 87: C10 (1982), 8031-
8038 (8 pages).
Application of fossil turbulence theory to the interpretation of 
the Dillon and Caldwell data set taken during the MILE 
expedition.  None of the microstructure patches presented 
are fully turbulent according to hydrodynamic phase 
diagrams derived from my 1980 theory.  Most are in the 
active-fossil or completely fossil quadrants, indicating severe 

43.  Gibson, C. H., "Fossil Turbulence in the Denmark 
Strait," J. Geophys. Res. 87: C10 (1982), 8039-8046 (8 
Application of fossil turbulence theory to Oakey's 
measurements of very large overturn patches with rather 
small e values in the Denmark Strait, with similar 
conclusions.  None of the patches presented are fully 
turbulent, or even close, again indicating severe 
undersampling of the turbulence and turbulent mixing 
process, and possibly explaining the discrepancy reported 
between the dropsonde estimates and those from bulk flow 
models (the "dark mixing" paradox).

44.  Gibson, C. H., "Turbulence in the Equatorial 
Undercurrent Core," in Hydrodynamics of the Equatorial 
Ocean (Proceedings of the 14th International  Liege 
Colloquium on Ocean Hydrodynamics, (Liege, May 1982), 
Vol. 36, J. C. H. Nihoul (Ed.), Elsevier Oceanography 
Series, Elsevier Publishing Company, Amsterdam (1983), 
131-154 (24 pages).
Intercomparison of towed body and dropsonde 
measurements in the core of the equatorial undercurrent and 
in the seasonal thermocline during the MILE expedition, 
showing the extremely intermittent lognormal distribution of 
the dissipation rates in these layers, and the high probability 
of underestimating the true mean values based on a small 
number of dropsonde samples.

45.  Washburn, L. and C. H. Gibson, "Horizontal 
Variability of Temperature Microstructure in the Seasonal 
Thermocline during MILE," J. Geophys. Res. 89 (1984), 
3507-3522 (16 pages).
Libe Washburn's thesis results, showing the extremely 
intermittent lognormal distribution of the temperature 
dissipation rate in the seasonal thermocline, with 
intermittency factors s2lnc ª 5.  Loop structures in the TS 
diagram suggest large horizontal eddies exist in a cascade 
that explains it.  

46.  Gibson, C. H. "Internal Waves, Fossil Turbulence, and 
Composite Ocean Microstructure Spectra," J. Fluid Mech. 
168 (1986), 89-117 (29 pages).
Reinterpretation of the paper by this title by Gargett et al.  
Fossil turbulence theory is used to show that the composite 
ocean shear spectra are subsaturated (not saturated as 
presented) internal waves at low frequencies, and fossil 
vorticity turbulence (not turbulence) at high frequencies.  
Typical temperature spectral forms of Gregg (1977) give the 
same interpretations.

47.  Gibson, C. H., "Oceanic Turbulence; Big Bangs and 
Continuous Creation," J. Physicochem. Hydrodyn., 8: 1 
(1987), 1-22 (22 pages).
Development of a fossil turbulence cascade model, based on 
published dropsonde measurements.

48.  Baker, M. A. and C. H. Gibson, "Sampling Turbulence 
in the Stratified Ocean: Statistical Consequences of Strong 
Intermittency,"  J. of Phys. Oceanogr., 17: 10 (1987), 
1817-1837 (22 pages).
 Mark Baker's thesis results.  All available ocean 
microstructure data for e and c are examined, and are shown 
to be well represented by extremely intermittent lognormal 
probability distributions, with intermittency factors s2lne and 
s2lnc in the range 3-7.  The consequences of neglecting 
effects of extreme intermittency on estimates of average 
values are examined [underestimates are quite likely-the 
mean to mode ratio for a lognormal is exp(3s2/2)].  
Confidence intervals for maximum likelihood estimators of 
mean values assuming lognormality are derived, and it is 
shown that the numbers of independent samples of e and c 
required by the s2 data to achieve 10% accuracy in estimates 
of mean values are in the range 100 to 10,000.

49.  Ashurst, W. T., A. R. Kerstein, R. M. Kerr and C. H. 
Gibson, "Alignment of vorticity and scalar gradient with 
strain rate in simulated Navier-Stokes turbulence", Phys. of 
Fluids, 30: 8 (1987), 2343-2353 (11 pages).
Direct numerical simulations of the Navier Stokes equations 
and scalar mixing are used to estimate average rate of strain 
statistics and the scalar gradient alignment statistics.  The 
principle g values were found to be in the ratio (3,1,-4), 
supporting the vermicelli turbulence model (different 
stretching in two directions, flattening in the other).

50.  Gibson, C. H., "Fossil Turbulence and Intermittency in 
Sampling Oceanic Mixing Processes," J. Geophys. Res. 92: 
C5 (1987), 5383-5404 (12 pages).
This paper summarizes all available laboratory and field 
information at the time of the Margaret River stratified 
turbulence symposium for comparison with fossil and non-
fossil turbulence models of stratified turbulence.

51.  Gibson, C. H.,  "Turbulence and Mixing in Stably 
Stratified Fluids,", Proceedings: International Conference on 
Fluid Mechanics, July 1-4,  Beijing, China Science Press 
(1987), 116-121 (6 pages).
Review of fossil turbulence theory for stratified flows.

52.  Gibson, C. H., W. T. Ashurst and A. R. Kerstein, 
"Mixing of Strongly Diffusive Passive Scalars Like 
Temperature by Turbulence,"  J.  Fluid Mech. 194 (1988), 
261-293 (33 pages).  
Compares numerical simulations of low Prandtl number 
turbulent mixing, as well as the turbulent temperature in 
mercury measurements of John Clay, with the Gibson 
(1968) and Batchelor, Howells and Townsend (1959) 
theories.  The evidence supports the Gibson (1968) k-3 
theory between the Obukov-Corrsin and Batchelor scales, 
but also indicates that the k-17/3 subrange predicted by the 
BHT (1959) theory also exists between the Batchelor and 
Kolmogorov scales.

53.  Gibson, C. H., "Hydrodynamic Phase Diagrams for 
Microstructure in Stratified Flows", in "Stratified Flows", 
Proceedings: Third International Symposium on Stratified 
Flows, Pasadena, Feb. 3-5, 1987, J. E. List and G. H. 
Jirka, Eds., American Society of Civil Engineers CP 775 
(1990), 276-290 (23 pages).  
A variety of techniques for classifying the hydrodynamic 
state of stratified microstructure as active turbulence, active-
fossil turbulence, or fossil turbulence are explored.

54.  Gibson, C. H., "Isoenstrophy Points and Surfaces in 
Turbulent Flow and Mixing," Proceedings of the IUTAM 
Symposium on Fundamental Aspects of Vortex Motion, 
Tokyo, Aug. 31-Sept. 4, 1987, Fluid Dynamics Research 3 
(1988), 331-336 (6 pages).  
The kinematics of turbulent vorticity fields are derived.  
Points of zero and minimal enstrophy (squared vorticity) are 
found to move approximately with the fluid, except for small 
viscous diffusion velocities.

55.  Gibson, C. H., "Evidence and Consequences of Fossil 
Turbulence in the Ocean", in Small Scale Turbulence and 
Mixing in the Ocean, Proceedings of the 19th International 
Liege Colloquium on Ocean Hydrodynamics (Liege, May 
1987), Vol. 46, J. C. H. Nihoul and B. M. Jamart (Ed.), 
Elsevier Oceanography Series, Elsevier Publishing 
Company, Amsterdam (1988), 319-334 (16 pages).  
Most of the microstructure measured in the ocean is shown 
to be fossilized, suggesting undersampling and possible 
underestimates of mean dissipation rates needed to predict 
turbulent diffusivities.

56.  McDougall, T., S. Thorpe and C. Gibson, Eds., 
"Small-Scale Turbulence and Mixing in the Ocean: A 
Glossary", in Small Scale Turbulence and Mixing in the 
Ocean, Proceedings of the 19th International Liege 
Colloquium on Ocean Hydrodynamics (Liege, May 1987), 
Vol. 46, J. C. H. Nihoul and B. M. Jamart (Ed.), Elsevier 
Oceanography Series, Elsevier Publishing Company, 
Amsterdam (1988), 3-9 (7 pages).  
Report of an effort by SCOR Working Group 69 on small 
scale turbulence in the ocean to define terms.  This meeting 
was organized by our Working Group.

57.  Gibson, C. H., "Comment on 'Reynolds number 
effects on turbulence in the presence of stable stratification', 
by A. E. Gargett", in Small Scale Turbulence and Mixing in 
the Ocean, Proceedings of the 19th International Liege 
Colloquium on Ocean Hydrodynamics (Liege, May 1987), 
Vol. 46, J. C. H. Nihoul and B. M. Jamart (Ed.), Elsevier 
Oceanography Series, Elsevier Publishing Company, 
Amsterdam (1988), 529-530 (2 pages).  
Comments on a very bad paper (although Ann's ideas are 
quite typical of the low level of understanding of stratified 
turbulence in the oceanographic microstructure community).  

58.  Gibson, C. H., "Oceanic and Interstellar Fossil 
Turbulence", in Radio Wave Scattering in the Interstellar 
Medium,  AIPCP 174, B. J. Rickett, J. M. Cordes D. C. 
Backer (Ed.) (1988), 74-79 (6 pages).  
Some speculations about turbulence in the interstellar 
medium and star formation.  Is there a connection between 
the size of solar systems and the scale of buoyancy inhibition 
of turbulence by the self gravitation of a protostar?

59.  Gibson, C. H., "Chapter 18. Turbulence, Mixing, and 
Microstructure",  in The Sea, Volume 9, Ocean Engineering 
Science, D. Hanes and B. LeMehaute, Eds., John Wiley and 
Sons, New York (1990), 631-659 (29 pages) 
Review of stratified turbulence fundamentals and the 
problems of sampling turbulence and turbulent mixing at 
sea.  Control volumes are used to explain the Reynolds 
(1895) decomposition postulates and the Osborn-Cox 
dissipation flux theory.

60.  Gibson, C.H., "Scalar Field Topology in Turbulent 
Mixing", Topological Fluid Mechanics, Proceedings of the 
IUTAM Symposium, Cambridge U. K., 1989, H. K. 
Moffatt and A. Tsinober, Eds., Cambridge University Press 
(1990), 85-94 (10 pages).
Discussion of the statistical geometry of scalar mixing 

61.  Gibson, C. H., "Turbulence," in Encyclopedia of 
Physics, R. G. Lerner and G. L. Trigg (Eds.), Addison-
Wesley Publishing Co., Inc. (1991), 1310-1314 (5 pages).  
This is an update of my 1981 entry on turbulence in this 
encyclopedia (see ref. 35).  

62.  Thomas, W. H. & C. H. Gibson, "Effects of Small-
Scale Turbulence on Microalgae", J. Applied Phycology, 2 
(1990), 71-77 (7 pages).
Marine biologists have known for thirty years that 
dinoflagellate growth is inhibited by turbulence in laboratory 
cultures, but this is the first attempt to quantify the 
turbulence threshold for growth inhibition for any species.  
Using a Coriolis force stabilized Couette flow (outer cylinder 
rotating) to produce a field of uniform rate-of-strain and a 
non-rotating control, the strain rates required to inhibit the 
growth were measured.  The possibility that the laboratory 
results are connected to red tide formation and wind 
turbulence is explored.

63.  Thomas, W. H. & C. H. Gibson, "Quantified Small-
Scale Turbulence Inhibits a Red Tide Dinoflagellate, 
Gonyaulax polyedra Stein", Deep Sea Research 37: 10 
(1990), 1583-1593 (11 pages).  
Details of the experiments are given, and comparison with 
widely scattered estimates of surface layer turbulence levels 
are made.

64.  Gibson, C.H., "Fossil Turbulence in Rotating, 
Stratified Flows", in Europhysics Conference Abstracts, On 
Turbulence, Proceedings of the 5th European Physical 
Society Liquid State Conference, Moscow, USSR, 16-21 
October 1989, K. Bethge, Ed. (1989), 227-230 (4 pages).  
This conference was organized to honor Kolmogorov, who 
died in 1988.  I gave the second talk, after Obukhov and 
before Monin, on the role of Kolmogorov's ideas about 
turbulence in oceanography.  The paper describes the fossil 
turbulence phenomenon in ocean turbulence due to buoyancy 
and Coriolis constraints to the growth of turbulence, and the 
remnant (fossil turbulence) internal waves and Coriolis-
inertial eddies that persist after oceanic turbulence is damped 
by these forces, and emphasizes the direct connection 
between my fossil turbulence theory and the Kolmogovov 
universal similarity hypotheses of unconstrained turbulence.

65.  Gibson, C. H., "Fossil Two-Dimensional Turbulence 
in the Ocean", in Turbulent Shear Flows, Vol. 7, Ed., F. 
Durst, W. C. Reynolds, Springer-Verlag (1991), 63-78 (8 
A discussion of fossil turbulence formation due to Coriolis 
force constraints of horizontal turbulence in the ocean, 
leaving remnant eddies that preserve information about the 
turbulence that produced them.

66.  Gibson, C. H., "Introduction to Scalar and Stratified 
Flows", in Turbulent Shear Flows, Vol. 7, Ed., F. Durst, 
W. C. Reynolds,, Springer-Verlag (1991), 3-7, (5 pages).  
An invited paper introducing a section of this book.

67.  Gibson, C. H., "Laboratory, Numerical, and Oceanic 
Fossil Turbulence in Rotating and Stratified Flows", J. 
Geophys. Res. (1991), 96: C7, 12,549-12,566 (18 pages).
A summary of the accumulated, and overwhelming, 
evidence demonstrating the stratified fossil turbulence 
phenomenon, and confirming the universal constants 
proposed in the Gibson (1980) theory.

68.  Gibson, C. H., "Kolmogorov Similarity Hypotheses 
for Scalar Fields:  Sampling Intermittent Turbulent Mixing in 
the Ocean and Galaxy", in Turbulence and stochastic 
processes: Kolmogorov's ideas 50 years on,  Proceedings of 
the Royal Society London, Ser. A, V434 (N1890) (1991), 
149-164 (16 pages).
An invited paper summarizing the extension of 
Kolmogorov's (1941) first and second universal similarity 
hypotheses for high Reynolds number turbulence to the case 
of scalar fields like temperature mixed by turbulence in my 
1968 turbulent mixing theory (see ref's 5 and 6), and 
comparing the Kolmogorov (1962) third hypothesis to our 
AKADEMIK KURCHATOV Cruise 51 tests for 
lognormality and the intermittency constant m for 
temperature dissipation in the seasonal thermocline off 
Monterey, California, using the Russian towed turbulimeter 
GRIF.  The data show very precise agreement with 
lognormality of c averaged over 10 octave scales from 1 to 
1000 meters, and m = 0.44 ± 0.01 from a direct test of 
s2lncr = m ln (L/r), in excellent agreement with our previous 
atmospheric measurements (see ref. 10 and ref. 12).

69.  Gibson, C. H., "Turbulence, Mixing, and Heat Flux in 
the Ocean Main Thermocline", J. Geophys. Res., 96: C7 
(1991), 20,403-20,420 (18 pages).
The Gregg (1977) microstructure measurements of Cox 
numbers in different seasons and years at the same site in the 
central Pacific are treated as representative independent 
samples of mixing in the main thermocline.  The 
distributions are extremely intermittent lognormals for all 
data and for depth classes, indicating mean values consistent 
with a constant vertical heat flux of about 6 Watts/m2.  This 
flux is about 30 times greater than values inferred without 
taking the extreme intermittency and lognormality of the data 
into account, and is consistent with bulk flow models of the 
thermocline such as the Munk (1966) Abyssal Recipe.

70.  Thomas, W. H., C. H. Gibson, "Effects of Quantified 
Small-Scale Turbulence on the Dinoflagellate, Gymnodinium 
sanguinum (splendens):  Contrasts with Gonyaulax 
(Lingulodinium) polyedra, and Fishery Implication", Deep 
Sea Research A, 39: 7-8 (1992), 1429-1437 (8 pages).
Tests of turbulence growth inhibition for a different species 
of dinoflagellate were made, and showed some similarities 
and differences in the growth response that have fishery 

71.  Lozovatsky, I. D, A. S. Ksenofontov, A. Y. Erofeev, 
C. H. Gibson, "Modeling of the Evolution of Vertical 
Structure in the Upper Ocean by Atmospheric Forcing and 
Intermittent Turbulence in the Pycnocline", J. of Marine 
Systems, 4: 2-3 (1993), 263-273 (11 pages).
Statistics of patch thicknesses and patch separations collected 
and interpreted by oceanographers of the Shirshov Institute 
of Oceanology, Moscow (and me).

72.  Lilover, M. J. ,  I. D Lozovatsky, C. H. Gibson, V. 
Nabatov, "Turbulence Exchange Through the Equatorial 
Undercurrent Core of the Central Pacific", J. of Marine 
Systems, 4: 2-3 (1993), 183-195 (13 pages).
First report of the 1991 cruise of the AKADEMIK 
KURCHATOV to the equatorial Pacific, describing 
dropsonde microstructure, CTD temperature and salinity and 
AD velocity profile stations at 15' intervals on 176 W from 
2 N to 2 S, GRIF towed microstructure profiling at the 
core, and BAKLAN dropsonde profiling of e and c 
microstructure near Baker and Howland Islands.  

73.  Gibson, C. H., V. Nabatov, R. Ozmidov, 
"Measurements of Turbulence and Fossil Turbulence Near 
Ampere Seamount", Dynamics of Atmospheres and Oceans, 
(1994), 175-204, (29 pages).
One problem oceanographers have expressed about my 
fossil turbulence interpretation of ocean microstructure is that 
none of the microstructure patches considered were ever 
found to be actively turbulent.  My explanation has been that 
such original turbulence patches are completely active for 
only a small fraction of their persistence time as partially or 
completely fossilized remnants, and that if you want to see 
fully active turbulence patches, you need to either take more 
data or go to a source of active turbulence, such as the 
shallow seamount of the present study.  According to my 
fossil turbulence theory, a completely active turbulence patch 
should have dissipation rate e greater than or equal to 
3LT2N3, where LT is the maximum density overturn scale 
and N is the stratification frequency.  It was found from 
BAKLAN dropsonde measurements of Nabatov and 
Osmidov that many turbulence patches with e > 3LT2N3 
could be found within less than a mile and below the crest of 
Ampere Seamount, but very few at greater distances.

74.  Gibson, C. H., "Some Unanswered Questions in Fluid 
Mechanics, The Direction of the Turbulence Cascade", Eds., 
L. M. Trefethen, R. L. Panton and J. A. C. Humphrey, 
ASME Winter Annual Meeting (1991), ASME paper 91-
WA-FE-1, (2 pages).  Internet ftp, login [anonymous], password [abcdef], cd 
pub/qbank, get p2, quit.
One of the myths of turbulence theory is that the direction of 
the turbulence cascade is from large scales to small, 
following the Richardson poem "Big whorls have little 
whorls, that feed on their velocity.  And smaller whorls have 
smaller whorls, and so on to viscosity (in the molecular 
sense)."  The actual turbulence goes the other way, 
according to the revised poem "Little whorls at viscous 
scales, form and pair with more of, whorls that grow by 
vortex forces.  Slava Kolmogorov!".  

75.  Thomas, W. H., M. Vernet, C. H. Gibson, 
"Mechanisms of Gonyaulax polyedra (Dinophycaea) 
Inhibition by Small-Scale Turbulence: Photosynthesis, 
Pigmentation, Cell Division, and Cell Sizes,"  J. of 
Phycology, (1994), (16 pages).
Growth inhibitions of cultures in rotating bottles were 
measured, and investigations of possible mechanisms carried 
out.  Photosynthesis and pigmentation are not affected, but 
cell splitting is strongly inhibited by turbulence as shown by 
the larger cell sizes.

76.  Gibson, C. H. and W. H. Thomas, "Effects of 
Turbulence Intermittency on Growth Inhibition of a Red 
Tide Dinoflagellate, Gonyaulax polyedra Stein,"  J. of 
Geophysical Research, Vol. 100, No. C12, pp. 24,841-
24,846, 1995.
The threshold for growth inhibition by average turbulence 
dissipation rates are decreased by factors of up to 100 by 
reducing the time interval of the turbulence to a small fraction 
of the day, but the turbulence time must be longer than 
several minutes.  This extreme sensitivity of growth to 
turbulence intermittency is compared to the strong negative 
correlations of wave heights (with intermittent turbulence) to 
weak correlations of wind speeds (with continuous 
turbulence) observed by our student Cyndy Tynan from 
phytoplankton population measurements on the SIO Pier.

77.  Bershadskii, A. and C. H. Gibson, "Singularities in 
Multifractal Turbulence-Dissipation Networks and Their 
Degeneration,"  Physica A (1995) (15 pages).
Catastrophe theory of singularities on dissipation networks, 
or caustic surfaces, is used to infer values of the 
Kolmogorov intermittency constant m in terms of the 
network fractal variability with increasing Reynolds number.  
For small Reynolds numbers the dissipation rate distribution 
is exponential and the effective m value is small: between 1/6 
and 1/3.  Degeneration of the caustics into a system of 
smooth filaments results in lognormality of e and a value of 
m = 1/2 according to multifractal asymptotics, close to the 
values for m and the distribution function for e observed at 
high Reynolds number experimentally (see ref.'s 10, 12, 
and 68).

78.  Gibson, C. H., "Introduction to Turbulent Flow and 
Mixing," Section 1.5 in Handbook of Fluid Mechanics and 
Machinery,  Joseph Schetz and Allen E. Fuhs (Eds.), John 
Wiley & Sons, pp. 83-90, 1996.
Invited introductory discussion of turbulence and mixing in 
Volume 1 of this three Volume handbook.  See 35 and 65.

79.  Gibson, C. H., "Stratified Flow," Section 13.7 in 
Handbook of Fluid Mechanics and Machinery,  Joseph 
Schetz and Allen E. Fuhs (Eds.), John Wiley & Sons, pp. 
832-841.  (Note:  Sect., Ed., & Publ. changed.)
Invited discussion of stratified flows for Volume 1 of this 
three Volume handbook.

80.  Gibson, C. H., "Turbulence in the ocean, atmosphere,
 galaxy, and universe", Applied Mechanics Reviews, vol 49,
 no 5, 299-315, 1996.
Reviews turbulence in natural flows, showing evidence of
 universal similarity from laboratory to intergalactic 
scales.  Questions the Jeans (1902) acoustic self-gravitational
 instability criterion as being incomplete.  Suggests condensation
 occurs at viscous and turbulent Schwarz scales which may be 
larger or smaller than the Jeans scale.  This leads to new and
different scenarios for structure formation in cosmology 
(and astrophysics).  The largest structures form first in the
 plasma epoch after the big bang, controlled by viscous forces,
 leaving a nested foamlike topology of matter from supercluster 
to galaxy masses.  At neutralization of the plasma about 300,000
 years after the big bang the entire universe turns to fog, with
 primordial fog particle (PFP) masses of about 10^22 kg.  These
 form the baryonic dark matter, since most of these PFPs remain 
as cold dark "moons" separated by 10^14 m in galactic halos.  The
 remaining dark matter in this model of a "flat" universe is in 
the form of gradually condensing WIMP particles (weakly interacting
 massive particles) in supercluster and cluster halos.  In
 astrophysics, powerful turbulence prevents condensation at the
 Jeans scale, so only huge blue stars can form in quasar jets and
 galactic disk blast waves.