Thermals with background rotation and stratification

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Abstract
Scaling analysis and experiments are used to study the evolution of thermals in the presence of background rotation. When the ambient environment is homogeneous, the thermal rises and expands until it reaches a critical height where the Rossby number becomes ∼ 1. The thermal then stops expanding and rises in a column. Both the critical height and column radius scale with (F0f-2)1/4. F0 is the initial thermal buoyancy and f is the Coriolis frequency. The thermal vertical velocity is independent of f. When the background is stratified with buoyancy frequency N, the thermal rises to a neutral buoyancy level which scales with (F0N-2)1/4. For N/f [Lt ] 0.6 column formation occurs before the thermal reaches the neutral level. For N/f [Gt ] 0.6 the thermal reaches the neutral level before rotation is important. In both regimes, geostrophic adjustment eventually causes the formation of a baroclinic vortex consisting of an anticyclonic lens of thermal fluid at the neutral level and cyclonic circulation below. The lens has Nh/fl ∼ 1. The lens thickness 2h and the radius l obey relations of the form (F0N-2)1/4 (N/f)m. However, the exponents m are different in the two regimes. The relevance of these results to deep-ocean convection and hydrothermal venting is discussed.