A Numerical Study of the Effects of Stratification on the Short-Wave Instability in a Vortex Pair

Daniel Mahoney
Master of Science, July 2002


Thesis Abstract

An aircraft in flight will generate a pair of counter-rotating wake vortices. A large aircraft can generate a wake vortex (or vortex pair) of considerable strength, which can pose a hazard to any craft which may encounter this wake vortex. The study of the mechanisms by which these vortices decay and breakdown is, therefore, of great practical importance. The evolution of the vortex pair is affected by its Reynolds number (which is a measure of the strength of the vortices) and the strength of stratification in the atmosphere.

Two flow instabilities, long wave and short wave, play an important role in the evolution of a counter rotating vortex pair. In certain situations it is thought that the short wave instability might play the most significant role in the evolution of the vortex pair. When stratification of the fluid is increased the growth rate of the short wave instability is greatly enhanced. This enhancement in growth rate is not fully understood.

The purpose of this work is to investigate the effect of varying levels of ambient stable stratification on the growth of the short wave instability. Direct Numerical Simulations are used to investigate the flow for a range of stratification levels (1< Fr < infinity) with a constant value of Reynolds number. The effect of stratification on the short wave instability is quantified by measuring wavelengths and growth rates.

An earlier onset and higher growth rate of the instability is found for a flow with stratification. With low levels of stratification (Fr > 1.5) an almost threefold increase in the growth rate of the instability is observed. In this case the wavelength of the instability is found to be the same as in the unstratified case. As the level of stratification is further increased (Fr < 1.5) the form of the instability becomes more complex (with the amplification of two wavelengths) with a slight reduction in the growth rate when compared with results for weak stratification.