Internally Heated Convection Experiments and Simulations

Steady Rayleigh–Bénard convection between stress-free boundaries

“…The conduction state is absolutely stable if for all admitted by the domain (see e.g. Goluskin (2015)).…”

Bounds on heat transport for convection driven by internal heating

“…2019). The dynamics of IH convection is also closely related, and sometimes equivalent, to that of flows driven by internal sources of buoyancy besides temperature, such as density stratification due to electromagnetic forces or chemical concentration differences (Goluskin 2016). IH convection therefore warrants study in its own right to enhance fundamental understanding of buoyancy-driven turbulence, yet has received relatively little attention in comparison with Rayleigh–Bénard convection.…”

“…A fundamental challenge in the study of IH convection, along with many other turbulent flows, is to characterise the flow's statistical properties as a function of its control parameters. Following previous work (Goluskin & Spiegel 2012; Goluskin 2016), we consider this problem in the idealised configuration illustrated in figure 1, where a horizontal layer of fluid between isothermal plates of equal temperature is heated uniformly at a constant rate. The only control parameters for this setting are the Prandtl number of the fluid, Pr , and the Rayleigh number based on the internal heating rate, R .…”

“…The ratio of the total (predominantly convective) heat flux to the conductive heat flux, which corresponds to a Nusselt number, is therefore . In contrast, quantifies the vertical asymmetry caused by the fluid's motion and is related to the heat fluxes and through the top and bottom boundaries by the exact relations (Goluskin 2016) …”

Model for classical and ultimate regimes of radiatively driven turbulent convection

“…Finally, it is questionable whether this type of modified RB experiment can be performed experimentally. Indeed, heating in volume can be achieved using either strong light (Lepot et al 2018), an electric current or even by fixing heating elements in the fluid (Kulacki & Goldstein 1972; Goluskin 2015; Goluskin & van der Poel 2016). On the contrary, cooling in volume is more difficult to achieve experimentally.…”