INVERSE CASCADES IN 2-DIMENSIONAL COMPRESSIBLE TURBULENCE .1. INCOMPRESSIBLE FORCING AT LOW MACH NUMBER

A fundamental property of forced, dissipative, two-dimensional incompressible Navier-Stokes (NS) systems is the dominance at long times of the longest wavelengths available to the flow. This dominance, attributed to an inverse cascade of energy with respect to enstrophy [Kraichnan, Phys. Fluids 10, 1417 (1967)], has been observed in spectrally accurate numerical simulations (see Refs. 5-7) of the incompressible NS equations. The numerical investigation of this behavior is extended to the weakly compressible regime by means of the fully compressible Fourier collocation code COMBOX with a solenoidal forcing function that imparts no net momentum and stirs the fluid in a wave-number band in the neighborhood of kf = 11. A comparison of spectral results from COMBOX simulations with an average Mach number of 0.22 with those from identically forced incompressible simulations, at Reynolds numbers ≤700, indicates (1) the compressible and incompressible wave-number dependences in both the energy cascading and enstrophy cascading regions are nearly identical; (2) in the compressible calculation, a dual power law is also observed in density and pressure fluctuations; and (3) continued (kf = 11) forcing leads to overall continued growth in the longest accessible velocity field wavelength, in both the incompressible and compressible cases.