Physics – Fluid Dynamics
Scientific paper
2000-06-07
Physics
Fluid Dynamics
50 pages of LaTeX (includes 25 pages of appendix), 12 postscript figures, submitted to Physics of Plasmas
Scientific paper
The unit of nonlinear interaction in Navier-Stokes and the Magnetohydrodynamic (MHD) equations is a wavenumber triad ({\bf k,p,q}) satisfying ${\bf k+p+q=0}$. The expression for the combined energy transfer from two of these wavenumbers to the third wavenumber is known. In this paper we introduce the idea of an effective energy transfer between a pair of modes through the mediation of the third mode and then find an expression for it. In fluid turbulence, energy transfer takes place between a pair of velocity modes, whereas in MHD turbulence energy transfer takes places between (1) a pair of velocity modes, (2) a pair of magnetic modes, and (3) between a velocity and a magnetic mode in a triad. In this paper we have obtained the expression for each of these transfers. We also show how the effective mode-to-mode energy transfer rate can be utilised to study energy cascades and shell-to-shell energy transfer rates.
Dar Gaurav
Eswaran Vinayak
Verma Mahendra K.
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