Abstract
The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the timedependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number Ra = 10^{9} and rotation parameters up to Q = 60 (where Q is a nondimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number Pr = 6.14 representative of water and enclosure heighttoradius ratio H/R = 0.4. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at Q ≈ 1 in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in Q sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest Q the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with Q. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over 5≲Q≲30, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.
Original language  English 

Pages (fromto)  135 
Number of pages  35 
Journal  Journal of Fluid Mechanics 
Volume  795 
DOIs  
Publication status  Published  May 2016 
Keywords
 Convection
 Instability
 Rotating flows
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