Force balance in rapidly rotating Rayleigh–Bénard convection

Abstract

The force balance of rotating Rayleigh–Bénard convection regimes is investigated using direct numerical simulation on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive view of the interplay between governing forces both in the bulk and near the walls. We observe, as in other prior studies, regimes of cells, convective Taylor columns, plumes, large-scale vortices (LSVs) and rotation-affected convection. Regimes of rapidly rotating convection are dominated by geostrophy, the balance between Coriolis and pressure-gradient forces. The higher-order interplay between inertial, viscous and buoyancy forces defines a subdominant balance that distinguishes the geostrophic states. It consists of viscous and buoyancy forces for cells and columns, inertial, viscous and buoyancy forces for plumes, and inertial forces for LSVs. In rotation-affected convection, inertial and pressure-gradient forces constitute the dominant balance; Coriolis, viscous and buoyancy forces form the subdominant balance. Near the walls, in geostrophic regimes, force magnitudes are larger than in the bulk; buoyancy contributes little to the subdominant balance of cells, columns and plumes. Increased force magnitudes denote increased ageostrophy near the walls. Nonetheless, the flow is geostrophic as the bulk. Inertia becomes increasingly more important compared with the bulk, and enters the subdominant balance of columns. As the bulk, the near-wall flow loses rotational constraint in rotation-affected convection. Consequently, kinetic boundary layers deviate from the expected behaviour from linear Ekman boundary layer theory. Our findings elucidate the dynamical balances of rotating thermal convection under realistic top/bottom boundary conditions, relevant to laboratory settings and large-scale natural flows.

Asymptotic scaling relations for rotating spherical convection with strong zonal flows

“…The force balances that were computed for our spherical simulations are similar to the results found by Aguirre Guzmán et al. (2021) for rapidly rotating convection with no-slip boundaries in Cartesian coordinates. In particular, Aguirre Guzmán et al.…”

Flow- and temperature-based statistics characterizing the regimes in rapidly rotating turbulent convection in simulations employing no-slip boundary conditions

“…The observed flow regimes are identified based on their flow-and temperature-based statistical properties (discussed in the present paper), their characteristic force balance (as we report in Ref. [17]), and their scale-by-scale kinetic energy transfer (as we discuss in Ref. [18]).…”

“…The domain-size vortical flows in panels (d) and (e) lead to large swirling patterns of temperature fluctuations; the cyclonic structure therein is indicated with a thin-lined box. The observed flow regimes are identified based on their flow-and temperature-based statistical properties (discussed in the present paper), their characteristic force balance (as we report in Ref [17][18]…”

Interplay between advective, diffusive and active barriers in (rotating) Rayleigh–Bénard flow

“…The viscous and buoyancy forces can be written in dimensionless form as In the spirit of the work of Aguirre Guzmán et al. (2021), we compute the coordinate-averaged root mean square (r.m.s.) of the two forces in both the vertical and radial directions.…”