Yushkov V. The Hamiltonian Formalism and Quantum Mechanical Analogy in the Probabilistic Description of Turbulence // Theoretical and Mathematical Physics. Moscow University Physics Bulletin. 2015, Volume 70, Issue 4, pp. 217-225 DOI: 10.3103/S00271349150

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.