Velocity gradient dynamics in compressible turbulence: Characterization of pressure-Hessian tensor Academic Article uri icon


  • Pressure-Hessian tensor produces the most significant difference between incompressible and compressible velocity gradient dynamics in turbulent flows. Characterization of pressure-Hessian tensor as a function of the level of compressibility is therefore of much interest. Using direct numerical simulation results, we demonstrate that the pressure-Hessian tensor behavior can be most exclusively characterized in terms of the compressibility parameter δ which is defined to be the growth-rate of dilatation-rate. A key compressibility effect is the distinct change in the alignment between pressure-Hessian and velocity gradient tensors with increasing δ. In incompressible turbulence, the pressure-Hessian eigenvectors exhibit a mild tendency to align at 45° angle with the principal directions of strain rate. With increasing δ, the pressure-Hessian tensor shows progressively stronger tendency to align along principal directions of the local strain-rate tensor. We show that this change in pressure-Hessian orientation causes the compressible velocity gradient dynamics to significantly differ from its incompressible counterpart. In incompressible turbulence, pressure mildly moderates the inherent gradient-steepening tendencies of the nonlinear inertial term. On the other hand, in highly compressible turbulence (extreme values of δ), pressure effects can lead to intense gradient steepening or smoothing depending upon the growth-rate of dilatation rate, thereby profoundly altering the cascade process. © 2013 AIP Publishing LLC.

author list (cited authors)

  • Suman, S., & Girimaji, S. S.

citation count

  • 10

publication date

  • December 2013