Geostrophic convective turbulence: The effect of boundary layers

Abstract

Rayleigh--Bénard (RB) convection, the flow in a fluid layer heated from below and cooled from above, is used to analyze the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotated while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier--Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\cdot 10^{10}$, a constant Prandtl number~$Pr=1$, and vary the Ekman number in the range $Ek=1.3\cdot 10^{-7}$ to $Ek=2\cdot 10^{-6}$ which satisfies both requirements of super-criticality and strong rotation. We focus on the differences between the application of no-slip vs. stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at~$Ek\approx 9\times 10^{-7}$ for~$Ra=1\times 10^{10}$ and at~$Ek\approx 3\times 10^{-7}$ for~$Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in~$Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.

Submitted to JFM

References in corpus (13)

• The unifying theory of scaling in thermal convection: The updated prefactors
• Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers vs Interior Dynamics
• Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers
• Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection
• Large-scale vortices in rapidly rotating Rayleigh-Bénard convection
• Heat transport and flow structure in rotating Rayleigh-Bénard convection
• Heat transport in the geostrophic regime of rotating Rayleigh-B{é}nard convection
• Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection
• The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-Bénard convection
• A nonlinear model for rotationally constrained convection with Ekman pumping
• Heat transport in rotating convection without Ekman layers
• Toroidal and poloidal energy in rotating Rayleigh-Bénard convection
• Breakdown of the large-scale wind in Γ=1/2 rotating Rayleigh-Bénard flow