On the determination of the absolute velocity of steady flows of a baroclinic fluid with applications to ocean currents

Abstract

The problem of determining the absolute velocity of marine currents, including its barotropic component, is revisited. A generalization of the classical Needler’s formula is discussed for a Boussinesq fluid and it is shown that the steady flow solution can be deduced from a variational principle that uses the constants of motion existing in the problem. A simple model of a steady flow is considered when the Bernoulli function consists of two terms. The first term is proportional to the square of Ertel’s potential vorticity and the second term is a quadratic function of the fluid buoyancy. This model is applied to mimic the circulation in the western Mediterranean Sea near the African coast. Alternatively, “potential temperature – salinity” coordinates are applied to construct the stream-tubes and infer the steady flow velocity in the simplest case of the Bernoulli function being proportional to the product of the above two variables.