Effect of hyperdiffusion on rotating Rayleigh-Bénard convection

We analyse the effect of a scale-dependent hyperdiffusivity in rotating Rayleigh-Benard convection. The hyperdiffusion (HD) is parameterised by a cutoff wavenumber k0 and a growth rate q to limit its effects to the smaller scales, enabling simulations to be conducted at more rapid rotation rates and buoyancy forcing (as measured by the Ekman number Ek and Rayleigh number Ra respectively) than in conventional direct numerical simulations (DNS). We have performed 107 simulations spanning the ranges E = 10-4 - 10-7 and Ra = 106 - 7 and directly compared HD and DNS heat transfer (measured by the Nusselt number N u), flow speeds P e, force balances and boundary layer thicknesses. We identify two different effects of HD that are particularly clear when k0 is below the dominant scale of the flow, k: at low supercriticality fRa, N u and P e are increased compared to DNS due to a weakening of the rotational constraint; at high Ra, Nu and Pe are decreased compared to DNS owing to suppression of energy at scales greater than k. The thermal boundary layer thickness changes in proportion to N u, while the mechanical boundary layer thickness is marginally affected because it is determined by a vertical balance, whereas HD is applied horizontally. Heat transfer diagnostics are more strongly affected by HD than flow diagnostics, while changing k0 has a greater impact on solution behaviour than changing q over the range of values studied. For all HD simulations with k0 3k, all diagnostics remain within the standard deviation of the DNS.