Sound and hydrodynamic turbulence in a compressible liquid

Canonical variables in which the potential and vortex motions are separated to a maximum degree are found for the Euler equations with small Mach numbers M = v, /c , ( v , is the characteristic turbulentpulsation velocity). The sound absorption decrement in a homogeneous isotropic turbulent medium calculated by the Wilde canonical diagram technique is r,, -M 2 ~ T / L ( L is the external scale of the turbulence pulsations). The spectral composition of sound emitted per unit tuburlence volume, ~ ( o ) o ' / ~ , is studied. The spectral energy density E, (a) of sound in equilibrium with the turbulence is calcula2ed. It is shown that the total energy density of the "equilibrium" sound is smaller by a factor M 3 than the energy density of the turbulent pulsations E,=. povT '. The effect of compressibility on the Kolmogorov spectrum of hydrodynamic turbulence is considered. This spectrum is of the form Jk = J , O + ~ J , , where J f k -"" is the Kolmogorov spectrum of an incompressible liquid and 6Jk -J, OM 2(kL)-2'3 is the compressibility correction.