Abstract
Motivated by astrophysical and geophysical applications, the classical problem of rotating Rayleigh-Bénard convection has been widely studied. Assuming a classical Fourier heat law, in which the heat flux is directly proportional to the temperature gradient, the evolution of temperature is governed by a parabolic advection-diffusion equation; this, in turn, implies an infinite speed of propagation of information. In reality, the system is rendered hyperbolic by extending the Fourier law to include an advective derivative of the flux—the Maxwell-Cattaneo (M-C) effect. Although the correction (measured by the parameter , a nondimensional representation of the relaxation time) is nominally small, it represents a singular perturbation and hence can lead to significant effects when the rotation rate (measured by the Taylor number ) is sufficiently high. In this paper, we investigate the linear stability of rotating convection, incorporating the M-C effect, concentrating on the regime of . On increasing for a fixed , the M-C effect first comes into play when . Here, as in the classical problem, the preferred mode can be either steady or oscillatory, depending on the value of the Prandtl number . For , the influence of the M-C effect is sufficiently strong that the onset of instability is always oscillatory, regardless of the value of . Within this regime, the dependence on of the critical Rayleigh number and of the scale of the preferred mode are explored through the analysis of specific distinguished limits.
- Received 29 April 2022
- Accepted 6 September 2022
DOI:https://doi.org/10.1103/PhysRevFluids.7.093502
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