Date of this Version
16TH EUROPEAN TURBULENCE CONFERENCE, 21-24 AUGUST, 2017, STOCKHOLM, SWEDEN.
I will present results from a series of DNS of compressible 2D turbulence forced in a narrow band of intermediate wavenumbers by a random solenoidal force δ-correlated in time. The simulations use an implementation of the piecewiseparabolic method (Colella & Woodward, 1984) to cover 400 sound-crossing times at a grid resolution of 81922 and then switch to a 7th order-accurate WENO7fi-split scheme (Kotov et al., 2016) in at 16,3842. This state-of-the-art shock capturing method delivers spectral-like quality of numerical solution at Mach numbers in a range from 0:3 to 0:7, providing scale separation sufficient to study all cascades in a single dual-cascade setting. Qualitatively, compressible 2D turbulence retains most of the physics already known for the incompressible case (Boffetta & Ecke, 2012), while adding more complexity to the problem. Vortices, populating the inverse energy cascade range, are destabilized due to the emission of sound waves (Broadbent & Moore, 1979). Emerging acoustic waves break into shocks, which amplify smallscale vorticity, and produce new vorticity through shock-shock interaction (Lighthill, 1955). Nonlinear acoustic vortex instability (Naugol’nykh, 2014) triggers spontaneous decay of coherent condensate. Complex interactions of vortices with waves control the scaling of the potential energy spectrum (Zakharov & Sagdeev, 1970). Acoustic turbulence induces direct energy cascade, closing a flux loop with classical solenoidal energy transport to large scales by an inverse cascade. Our main focus is on applications to large-scale compressible turbulence in galactic disks (Bournaud, et al., 2010), but results are also relevant to laboratory experiments with turbulence in moving soap films and in fluid layers.