Transfer at Rough Sheared Interfaces

Transfer of extensities such as heat across sheared rough interfaces is considered, with particular attention to roughnesses characterized by a broad hierarchy of length scales. We analyze as a concrete example the corrections to the Nu-Ra dependence in high Rayleigh number convection cells induced when the thermal layer thickness λ~LRa^-β is of the order of the conducting walls roughnesses ξ. We show that, provided ln(5Pr)Pr1/2LξRa^1/2-2β, the increase of exchange surface area due to the covering of the rough surface by the thermal layer may significantly alter the transfer relationship in absolute value, and in law.