A general mutual helicity formula

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 disjoin t 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 o f the vector fields across corresponding spanning surfaces inside the domai ns.