http://arxiv.org/abs/1709.00814
Large-scale turbulence in fluid layers and other quasi two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here we consider turbulence at finite Mach numbers when interaction between acoustic waves and vortices is substantial. We employ solenoidal pumping at intermediate scales and show how both direct and inverse energy cascades are formed starting from the pumping scale. We show that there is an inverse cascade of kinetic energy up to a scale, $\ell$, where typical velocity reaches the speed of sound; that creates shock waves which provide for a compensating direct cascade. When the system size is less than $\ell$, the steady state contains a system-size pair of long-living condensate vortices connected by a system of shocks. Thus turbulence in fluid layers processes energy via a loop: most energy first goes to large scales via vortices and is then transported by waves to small-scale dissipation.
G. Falkovich and A. Kritsuk
Tue, 5 Sep 17
21/76
Comments: 11 pages, 7 figures; Accepted to Phys. Rev. Fluids as Rapid Communication