Vortex pairing and mixing in stratified shear flows

Kelvin-Helmholtz (KH) instabilities are an important source of mixing in oceans, lakes and the atmosphere. The process of vortex pairing can increase the amount of mixing. First, the effects of initial conditions on vortex pairing and mixing are studied by running Direct Numerical Simulations with a variety of initial perturbations. It is shown that when the subharmonic component of the perturbation is out of phase relative to the KH mode, vortex pairing is delayed or even eliminated. The amount of mixing in the simulations where the subharmonic mode is out of phase is approximately half of that in the simulations where the subharmonic mode is in phase. The time of pairing is also found to be sensitive to the phase of the subharmonic mode. A slight change of the phase can change time of pairing significantly when the subharmonic mode is close to being out of phase. Second, the effects of Prandtl number on KH instabilities, vortex pairing and mixing are studied. It is found that KH instabilities and vortex pairing are suppressed at higher Prandtl numbers, which tends to reduce the amount of mixing. This effect is counteracted by enhanced three-dimensional motions in higher Prandtl number flows. However, the general trend is for mixing and mixing efficiency to decrease as Prandtl number is increased.