A general mutual helicity formula

Abstract

In this paper, we consider the mutual helicity of a pair of divergence–free vector fields defined on, and tangential to, the boundaries of two disjoint domains in 3–space. Generalizing previous results of Moffatt and Laurence & Avellaneda, we derive a simple formula for this helicity in terms of the linking numbers of curves on the boundary of the two domains, and fluxes of the vector fields across corresponding spanning surfaces inside the domains.