Simple theoretical and experimental study of convection with some geophysical applications and analogies

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Abstract
A plane horizontal layer of a fluid with depth d is considered into which heat is introduced. Within the Boussinesq approximation an exact expression is obtained for the efficiency of convection γ in transforming the rate of heat supplied into the generation of kinetic energy. It agrees with results of numerical and laboratory experiments whose data can be used to calculate this value. In laboratory experiments γ is usually of order 10−8 to 10−6. Using this quantity estimates are obtained for the r.m.s. velocity of convective motions and τ. Applications of the results obtained are briefly discussed for studies of heat and mass transfer in the ocean and of convection in the Earth's mantle.In the last section some general properties are considered for various forced flows, convection, turbulence and some types of atmospheric circulation, that allow one to formulate a ‘rule’ of the fastest response, which asserts that the kinetic energy of a fluid system is of order of the supplied power times the fastest relaxation time which the system possesses.

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