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Abstract A conservative quantity is found as an integral of a component of the vorticity equation and used to formulate a non‐linear theory of steady, two‐dimensional convection in shear. The steering‐level and propagation speed are determined in terms of a Richardson number and a density‐scaling parameter. Case studies indicate a favourable agreement between theory and observation, especially where the Richardson number is of order unity. The parcel theory of convection is extended and the importance of the horizontal pressure gradient as a control on the updraught intensity is discussed quantitatively. Heat and momentum transfer laws are obtained in terms of the mean flow parameters, and define a non‐Fickian transfer.
Moncrieff et al. (Sat,) studied this question.