Spectral Properties, coherent structures and correlations in Nearly Incompressible Hydrodynamics

Details Spectral Properties, coherent structures and correlations in Nearly Incompressible Hydrodynamics Spectral Properties, coherent structures and correlations in Nearly Incompressible Hydrodynamics

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufmsh32d..06d&link_type=abstract

American Geophysical Union, Fall Meeting 2003, abstract #SH32D-06

Computer Science

Sound

2149 Mhd Waves And Turbulence, 2164 Solar Wind Plasma

Scientific paper

Observational evidence from Voyager and Helios space-craft indicate that density fluctuations in the Solar wind follow Kolmogorov-like spectrum which cannot be explained on the basis of purely incompressible models. These observations have led to the exploration of the relationship between density fluctuations and incompressible fluid models. This has resulted in the development of nearly incompressible (NI) hydrodynamics, which retains compressibility to first-order, producing (magneto)acoustic modes as well as convective modes. Depending upon the amplitude of thermal, pressure and density fluctuations there exist two distinct approaches to incompressibility. When density and temperature dominate the pressure fluctuations, the NI regime is called heat fluctuation dominated (HFD). On the other hand, when all the fluctuations are comparable heat fluctuation modified (HFM) NI regime results. The HFD regime predicts density-temperature anti-correlations, while HFM shows a `modified pseudosound' relation. NI hydro and MHD have been surprisingly successful in the solar wind where predicted correlation are seen frequently and predicted anisotropies are observed. However, the basic nonlinear development of NI hydro and MHD remain completely unexplored. We have therefore initiated a comprehensive project to explore the nonlinear features of NI theory. We discuss three sets of results. 1) We find that the density fluctuations are described in the HFM limit by passive scalar dynamics rather than pseudosound dynamics, resulting in a density spectrum which is globally Kolmogorov-like with an exponent close to -5/3. The density fluctuations are found to be anisotropic in wavenumber space. 2) The background low frequency and first order high frequency NI modes mutually interact to produce nonlinear shear flows, also known as zonal flows. The zonal flows are primarily generated by effective Reynolds stresses. 3) Finally, for the HFD case, we show that the nonlinear interaction of the incompressible and nearly incompressible modes leads to a turbulent relaxation in which self-organization through an inverse cascade mechanism results in the formation of large scale compressive coherent vortices. The density and thermal fluctuations are also found to be anti-correlated.

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