The Hamiltonian formalism and quantum-mechanical analogy in the probabilistic description of turbulence

Abstract

It is shown here that (i) the interaction of adiabatic waves with incompressible turbulence makes it possible to statistically describe the transfer of the energy of turbulent pulsations over the spectrum, (ii) the fundamental parameter that allows the effect of adiabatic motions on incompressible turbulence to be parameterized is the entropy dissipation coefficient in the equation that is called the Obukhov equation in this paper, and (iii) the generalized coordinates or canonical variables of the Zakharov equation should be interpreted as wave functions.