  We present hydrodynamic equations of compressible fluids in gravity as a
generalization of those in the Boussinesq approximation used for nearly
incompressible fluids. They account for adiabatic processes taking place
throughout the cell (the piston effect) and those taking place within plumes
(the adiabatic temperature gradient effect). Performing two-dimensional
numerical analysis, we reveal some unique features of plume generation and
convection in transient and steady states of compressible fluids. As the
critical point is approached, overall temperature changes induced by plume
arrivals at the boundary walls are amplified, giving rise to overshoot behavior
in transient states and significant noises of the temperature in steady states.
  The velocity field is suggested to assume a logarithmic profile within
boundary layers. Random reversal of macroscopic shear flow is examined in a
cell with unit aspect ratio. We also present a simple scaling theory for
moderate Rayleigh numbers.

Soft Condensed Matter