Modulated Thermal Convection
Natural systems are often driven by forces that vary over time. For instance, the alternation between day and night gives rise to a 24 h cycle of heating and cooling, which has an impact on the atmospheric convection as well as on our oceans. Hence, studying the effects of thermal modulation is fundamental to the understanding of many geo- and astrophysical flows.
Periodically Modulated Thermal Convection (Temporal)
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In periodically modulated Rayleigh–Bénard convection, the bottom temperature is modulated by a sinusoidal signal of the form:
The effect of the modulation can be classified in three regimes: (i) A regime where the modulation is too fast to affect Nu (high frequency); (ii) a moderate modulation regime, where Nu increases with increasing frequency and reaches its maximum, and (iii) a slow modulation regime, where Nu decreases with further decreasing frequency (
Travelling thermal wave modulation (temporal + spatial)
Spatially periodic systems like the Earth are often subjected to travelling waves. One way to model those systems is to apply thermal waves at the fluid layer surface, then the boundary conditions can be cast in the form:
As in the case of periodically modulated thermal convection, the modulation gives rise to heat and momentum transport enhancement for certain frequencies. Beside that, the travelling waves generate zonal flows, i.e. mean horizontal flows. These zonal flows can be rather strong and even exceed the phase velocity of the travelling wave. It can be shown that these zonal flows are directed opposite to the travelling waves, if convection is weak. However, if convection is strong, the zonal flows are generally directed in the same direction as the thermal wave (
Further reading