Convection in a box: on the dependence of preferred wave-number upon the Rayleigh number at finite amplitude

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Abstract
Using Stuart's shape assumption and a condition of maximum heat transport it is found that the preferred number of finite roll cells present in Bénard convection in athree-dimensional rectangular boxtends todecreasewith increasing supercritical Rayleigh number in contradiction to the behaviour in an infinite layer but in accordance with experimental observation.This ‘end effect’ might explain the similar observation of wave-number decrease in the Taylor instability between rotating cylinders.

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