Studying of Helical Turbulence Self-Organization Based on 3D-Generalization of Hasegawa-Mima Equation

Abstract

The important property of hydrodynamic turbulence is the helicity h which is defined by and can be considered as a some ordering parameter of turbulent motions. In the framework of ideal hydrodynamics equations

$$ \partial \overrightarrow v /\partial t + (\overrightarrow v \overrightarrow v ) = - \overrightarrow v P/p,P = {P_{0}}{(p/{p_{0}})^{{\gamma ,}}}$$

$$ \partial p/\partial t + divp\overrightarrow v = 0$$

$$ \partial h/\partial t + divh\overrightarrow v = div[\overrightarrow w ({v^{2}}/2 - B)],$$

((1))

$$ w = curl\overrightarrow {v,} B = \int\limits_{{{P_{0}}}}^{P} d P/p$$