Nearly incompressible fluids: Decay of solar wind density fluctuations

The evolution of density fluctuations throughout the solar wind is investigated as the basis of a newly developed theory of nearly incompressible hydrodynamics for an inhomogeneous flow. The model is explored using two‐dimensional numerical simulations. The lowest‐order density fluctuations (absent in the original homogeneous nearly incompressible theory) obey a passive scalar evolution equation with an additional source term that results from coupling to the large‐scale inhomogeneous mean density gradient. The importance of this source term is explored, and we estimate analytically an upper bound for the maximum possible effect of a source term for nearly incompressible flows with an inhomogeneous background (static and spherically symmetric). For typical solar wind parameters, we show that this effect is rather weak beyond 0.1 AU and that the density fluctuations can be described sufficiently accurately as a pure passive scalar. Our simulations identify the sensitive dependence of density fluctuation evolution on typical initial length‐scale ratio of scalar (density) and velocity fields, an effect known from the theory of passive scalar decay and experimentally measured in grid‐generated turbulence. It has long been thought that the variance in the density fluctuations ( δρ ) 2 should decay in the manner analogous to the mean background density, implying that with heliocentric distance ( δρ ) 2 ∝ R −4 throughout the heliosphere. Analysis of plasma data obtained by the Voyager spacecraft by Bellamy et al. (2005) showed that the density fluctuations decay much more slowly than R −4 and the decay rate exhibits a flattening between 20–30 AU and a possible rise afterward. A possible mechanism to reduce the decay rate within 30 AU was suggested to be turbulence driven by stream‐stream interactions followed by more dominant pickup ion interactions beyond 30 AU. Here we show that the variance in the density fluctuations as described by the inhomogeneous nearly incompressible theory evolves essentially independently of the mean density background with a decay rate that reduces and possibly levels off with increasing heliocentric distance.