Nearly incompressible magnetohydrodynamics, pseudosound, and solar wind fluctuations

Recent theoretical studies have led to an improvement of our understanding of the behavior of a compressible magnetofluid with an adiabatic equation of state, in the limit of low plasma frame Mach number. Under certain assumptions the lowest‐order behavior is that of incompressible magnetohydrodynamics (MHD), associated with small nonpropagating “pseudosound” density fluctuations. Departures from incompressibility include magnetoacoustic fluctuations, appearing at the same order as the pseudosound. In the present paper the simplest nearly incompressible MHD theory, with a polytropic equation of state, is reviewed, with an emphasis on observable consequences, particularly for solar wind turbulence. A central feature of the theory is the development of a relationship between the spectra of density fluctuations and of magnetic and velocity fluctuations. Here this relationship is extended to include uniform magnetic field effects, the possibility of anisotropic turbulence, and the influences of magnetic and cross helicities. Consequences of the theory, including Mach number scalings of density fluctuations and their wave number dependence, the anticorrelation of mechanical and magnetic pressure, and the reduction of density fluctuations in Alfvénic periods, are discussed in terms of Voyager solar wind observations. Finally, we present results of a simulation using a two‐dimensional compressible MHD code that illustrate the appearance of similar anticorrelations.