Stabilizing action of pressure in homogeneous compressible shear flows: effect of Mach number and perturbation obliqueness

Compressibility exerts a stabilizing influence on a variety of high-speed shear flows such as turbulent mixing layers, transitioning boundary layers and homogeneously sheared turbulence. An important stabilizing feature that is common amongst all shear flows is the velocity–pressure interaction dynamics. In this study, velocity–pressure interactions of individual perturbation or fluctuation modes are investigated using direct numerical simulations and linear analysis in high-Mach-number homogeneous shear flow. For a given perturbation wave mode, the action of pressure is shown to depend on two important factors: the orientation of the perturbation wavevector with respect to the shear plane and the Mach number. It is shown that the streamwise perturbation wave mode rapidly develops a high level of kinetic energy but is self-limiting owing to the action of pressure. On the other hand, the energy of spanwise perturbation wave modes grows unaffected by pressure or Mach number. Oblique modes combine spanwise and streamwise characteristics and are shown to be chiefly responsible for stabilizing effects seen in shear flows. Three regimes of obliqueness of different linear stability characteristics are identified. The critical role of perturbation obliqueness on stabilization is established.

Combined Effect of Viscosity, Surface Tension and Compressibility on Rayleigh-Taylor Bubble Growth Between Two Fluids

The combined effect of viscosity, surface tension, and the compressibility on the nonlinear growth rate of Rayleigh-Taylor (RT) instability has been investigated. For the incompressible case, it is seen that both viscosity and surface tension have a retarding effect on RT bubble growth for the interface perturbation wave number having a value less than three times of a critical value (kc=(ρh-ρl)g/T, T is the surface tension). For the value of wave number greater than three times of the critical value, the RT induced unstable interface is stabilized through damped nonlinear oscillation. In the absence of surface tension and viscosity, the compressibility has both a stabilizing and destabilizing effect on RTI bubble growth. The presence of surface tension and viscosity reduces the growth rate. Above a certain wave number, the perturbed interface exhibits damped oscillation. The damping factor increases with increasing kinematic viscosity of the heavier fluid and the saturation value of the damped oscillation depends on the surface tension of the perturbed fluid interface and interface perturbation wave number. An approximate expression for asymptotic bubble velocity considering only the lighter fluid as a compressible one is presented here. The numerical results describing the dynamics of the bubble are represented in diagrams.

DEPENDENCE OF HAMILTONIAN CHAOS ON PERTURBATION STRUCTURE

In this paper, we considered a Hamiltonian dynamical system consisting of a steady wave and a perturbation wave and studied the dependence of spatial patterns of chaos on the perturbation structure (i.e., the wave numbers of the perturbation wave). The system came from the passive wave mixing and transport problem. In order to investigate this dependence, we first did some simple mixing experiments with initially a small blob and calculated the correlation dimensions. Secondly we used Lyapunov exponents to identify the chaotic regions and the invariant tori and computed the histograms or PDFs (Probability Distribution Functions) to characterize the Hamiltonian chaos for different perturbation structure. We found that this dependence was very complicated and the complexity increases with the perturbation structure. This dynamical system became more chaotic with increase in the wave numbers. The fascinating patterns of the Hamiltonian chaos for various perturbation structures were presented. The spatial pattern of chaos on the isentropic surface of the atmosphere was given. Implications of the results of the chaotic wave mixing and transport in climate dynamics, atmospheric chemistry, aeronomy and large scale dynamics of geophysical fluid flows were briefly discussed.