Volume and Mass Transport across Isosurfaces of a Balanced Fluid Property

Abstract

This work provides the general theory of the volume and mass conservation in terms of its transport across surfaces (open or closed) defined by a constant value of an oceanographic property obeying a balance law. This fluid property can be any spatial density ? (amount of quantity per unit volume), or its specific value ?? ≡ α? (amount of quantity per unit mass, where α is the specific volume). The main expressions obtained relate the volume transport across a ?-surface to the flux of the quantity (h?) across the ?-surface boundary, and the mass transport across a ??-surface to the flux h? across the ??-surface boundary. These expressions differ, in general, from the volume and mass conservation of the ?-surface, being however equivalent for closed (unlimited) ?-surfaces. The main expressions are generalized to the three-dimensional case, and the relation to previous results is discussed.