Dependence of the stationary kinetic energy on initial conditions

Determine whether the kinetic energy of the statistically stationary state of Rayleigh–Bénard convection is independent of the initial vertical position of the fluid’s center of mass, particularly under the weakly controlled evolution considered in the paper.

Background

The paper questions whether the statistically stationary state of Rayleigh–Bénard convection is fully determined by the usual control parameters. In its energy analysis, it considers an evolution in which the fluid begins with a prescribed initial temperature and density profile, and notes that the final kinetic energy could potentially depend on the initial height of the fluid’s center of mass.

The authors identify independence from this initial condition as an unresolved issue. Establishing the answer is important for determining whether statistically stationary Reynolds and Nusselt numbers are intrinsic functions of the control parameters or retain memory of the preparation of the system.