Role of pressure in nonlinear velocity gradient dynamics in turbulence.

To identify and understand the effect of pressure on turbulence velocity gradient dynamics, we study the velocity gradient evolution with the inviscid three-dimensional Burgers equation and the restricted Euler equation (REE). While the REE represents the incompressible limit of turbulence, the Burgers equation is taken to be the infinite Mach number model for the Navier-Stokes equation wherein the time scale of flow inertia is very small compared to that of pressure. Analytical fixed-point solutions for the velocity gradient tensor are obtained in the two cases. The results are compared and contrasted to isolate the role of pressure in shaping velocity gradient behavior. Of particular interest is the influence of pressure on (i) the strain rate eigenvalues; (ii) the sign of the intermediate principal strain rate; (iii) the tendency of vorticity to align with the intermediate principal strain rate; and (iv) the energy cascade direction. Importantly, the study provides valuable insight into the velocity gradient dynamics in highly compressible turbulence.

Role of pressure in nonlinear velocity gradient dynamics in turbulence. Academic Article