Nearly incompressible hydrodynamics and heat conduction

By means of an asymptotic analysis, two distinct approaches to incompressibility are found for a low-Mach-number ideal fluid, distinguished according to the relative magnitudes of temperature, density, and pressure fluctuations. For heat-conduction-dominated-fluids, temperature and density fluctuations are predicted to be anticorrelated, and the classical passive scalar equation for temperature is recovered, whereas a generalized ``pseudosound'' relationship for the fluctuations is found for heat-conduction-modified fluids, together with a modified thermal equation. The full set of nearly incompressible dynamical equations is described.