Volume and Mass Transport across Isosurfaces of a Balanced Fluid Property

Álvaro Viúdez University of St. Andrews, St. Andrews, Fife, United Kingdom

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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 ϕ (amount of quantity per unit volume), or its specific value ϕ̂αϕ (amount of quantity per unit mass, where α is the specific volume). The main expressions obtained relate the volume transport across a ϕ-surface to the flux of the quantity (hϕ) across the ϕ-surface boundary, and the mass transport across a ϕ̂-surface to the flux hϕ across the ϕ̂-surface boundary. These expressions differ, in general, from the volume and mass conservation of the ϕ-surface, being however equivalent for closed (unlimited) ϕ-surfaces. The main expressions are generalized to the three-dimensional case, and the relation to previous results is discussed.

Corresponding author address: Dr. Álvaro Viúdez, School of Mathematical and Computational Sciences, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom.

Email: alvarov@dcs.st-and.ac.uk

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 ϕ (amount of quantity per unit volume), or its specific value ϕ̂αϕ (amount of quantity per unit mass, where α is the specific volume). The main expressions obtained relate the volume transport across a ϕ-surface to the flux of the quantity (hϕ) across the ϕ-surface boundary, and the mass transport across a ϕ̂-surface to the flux hϕ across the ϕ̂-surface boundary. These expressions differ, in general, from the volume and mass conservation of the ϕ-surface, being however equivalent for closed (unlimited) ϕ-surfaces. The main expressions are generalized to the three-dimensional case, and the relation to previous results is discussed.

Corresponding author address: Dr. Álvaro Viúdez, School of Mathematical and Computational Sciences, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom.

Email: alvarov@dcs.st-and.ac.uk

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