How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence

Abstract

Large-scale turbulence in fluid layers and other quasi-two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces a 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 the 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 a typical velocity reaches the speed of sound; this 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.

11 pages, 7 figures

References in corpus (6)

• Theory of Star Formation
• Universal profile of the vortex condensate in two-dimensional turbulence
• Vortices in Thin, Compressible, Unmagnetized Disks
• The structure and statistics of interstellar turbulence
• Isentropic thermal instability in atomic surface layers of photodissociation regions
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Cited by in corpus (7)

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• Exact relations for energy transfer in self-gravitating isothermal turbulence
• Conformal invariance of weakly compressible two-dimensional turbulence
• The contribution of dilatational motion to energy flux in homogeneous compressible turbulence
• $\lambda$-Navier-Stokes turbulence
• Real Schur flow computations, helicity fastening effects and Bagua-pattern cyclones
• Intermittency and non-universality of pair dispersion in isothermal compressible turbulence