On statistical equilibrium in helical fluid flows
Abstract. The statistical mechanics of 3-D helical flows is re-examined for a continuum truncated at a top wavenumber. Based on the principle of equipartition of the flow enstrophy between helical modes, the emerging (i) energy spectrum law "–2" and (ii) formal mathematical analogy between the helicity and the thermodynamic entropy are discussed. It is noted that the "–2" scaling law is consistent with both spectral equilibrium and spectral cascade paradigms. In an attempt to apply the obtained results to a turbulent flow regime within the Earth's outer liquid core, where the net helicity of a turbulent flow component is presumably explained by Earth's rotation, it has been noticed that it is the energy spectral law "–1", but not "–2", which is likely realized there and within the logarithmic accuracy corresponds to the case of the velocity structure function [u(l)]2 independency on the spatial scale l, the latter is consistent with observations. It is argued that the "–1" scaling law can also be interpreted in terms of the spectral equilibrium and it is emphasized that the causes of the likely dominance of the spectral law "–1" over the spectral law "–2" in this geophysical application deserve further investigation and clarification.
