Triangle principle of inertial transport in incompressible turbulence

Abstract

It is proved that the inertial energy fluxes among any three Fourier components, where one wave vector is the sum or difference of the other two wave vectors, must be closed. This result is called triangle principle because such three vectors can form a triangle. Although the global energy conservation of inertial transport, which states that inertial transport does not change the total energy but only redistributes the energy among different Fourier components, is well known, the triangle principle gives the detailed mechanism for the global energy conservation and can therefore be called detailed energy conservation in inertial transport. A mechanism, similar to Darwin’s natural selection, for the establishment of the quasi-equilibrium energy spectrum of dissipation range is discussed. Thus, the present analysis gives one example to show how detailed dynamical analysis may help to understand the establishment of certain statistical regularity.