Isotropic and anisotropic turbulence in Clebsch variables

Three-dimensional turbulence of incompressible fluid is described by using Clebsch canonical variables. This reveals the families of new local integrals of motion so that there are additional cascade spectra besides the energy cascade. A weakly anisotropic spectrum of developed turbulence is shown to be as universal as isotropic Kolmogorov spectrum. The correlation functions of three-dimensional incompressible turbulence approach their isotropic values in the inertial interval so that the share taken by the anisotropic parts of velocity correlators decrease with the wavenumber as , which satisfactorily fits the experimental data. The complementarity of the turbulence description in Clebsch and velocity variables is demonstrated.