Nearly incompressible theory and large scale flows

Details Nearly incompressible theory and large scale flows Nearly incompressible theory and large scale flows

Aug 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aipc..932...45h&link_type=abstract

TURBULENCE AND NONLINEAR PROCESSES IN ASTROPHYSICAL PLASMAS; 6th Annual International Astrophysics Conference. AIP Conference P

Astronomy and Astrophysics

Astrophysics

Particle Emission, Solar Wind, Solar Wind Plasma, Sources Of Solar Wind, Mhd Waves, Plasma Waves, Turbulence

Scientific paper

The nearly incompressible theory of hydrodynamics has been generalized to flows which include a time-independent large-scale inhomogeneous background, such as the solar wind (Hunana, Zank, Shaikh, Phys. Rev. E 74, 026302, 2006). In contrast with the homogeneous case, the expansion of the fully compressible Navier-Stokes equations in powers of sonic Mach number leads at the lowest order to a new system of inhomogeneous equations (referred to as locally incompressible). In this work, we numerically investigate this new inhomogeneous description for two dimensional freely-decaying turbulence. We concentrate on the decay of the power spectrum for density fluctuations with an inhomogeneous density background in one direction that is proportional to 1/r2. Nearly incompressible theory predicts that the density fluctuations δρ behave at the leading order as a passive scalar, with an additional source term produced by coupling to the large-scale inhomogeneous background. In this preliminary work, it is shown that the source term is responsible for a slower <δρ2> power spectrum decay, which has interesting implications for the ``anomalous'' observations of decaying density Voyager spectra described by Bellamy, Cairns, Smith, JGR 110, A10104, 2005.

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