Find in Library

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 '&ndash;2' and (ii) formal mathematical analogy between the helicity and the thermodynamic entropy are discussed. It is noted that the '&ndash;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 '&ndash;1', but not '&ndash;2', which is likely realized there and within the logarithmic accuracy corresponds to the case of the velocity structure function [<i>u</i>(<i>l</i>)]² independency on the spatial scale <i>l</i>, the latter is consistent with observations. It is argued that the '&ndash;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 '&ndash;1' over the spectral law '&ndash;2' in this geophysical application deserve further investigation and clarification.