Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 12 1 2005 10.5194/npg-12-75-2005 http://www.nonlin-processes-geophys.net/12/75/2005/ http://www.nonlin-processes-geophys.net/12/75/2005/npg-12-75-2005.html http://www.nonlin-processes-geophys.net/12/75/2005/npg-12-75-2005.pdf 75 81 2005-01-25 Modeling of short scale turbulence in the solar wind V. Krishan S. M. Mahajan Indian Institute of Astrophysics, Bangalore 560 034, India Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA The solar wind serves as a laboratory for investigating magnetohydrodynamic turbulence under conditions irreproducible on the terra firma. Here we show that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfv&#233;nic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum - the Kolmogorov branch <i>f</i>^-5/3 steepening to <i>f</i>^-&alpha;₁ with <!-- MATH $\alpha_1{\simeq}3{-}4$ --> <IMG WIDTH="61" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" src="http://www.nonlin-processes-geophys.net/12/75/2005/npg-12-75-img3.gif" ALT="$alpha_1{simeq}3{-}4$"> on the high frequency side and flattening to <i>f</i>^-1 on the low frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD Shear Alfv&#233;n waves. The spectrum of the concomitant whistler type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of equipartition of energy through the so called Alfv&#233;n ratio acquires a new status through its dependence, now, on the spatial scale.