English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Explicit expressions of the 3D velocity field in terms of the conservedquantities of ideal fluid thermocline theory, namely Bernoulli function,density, and potential vorticity, are generalised here to a compressible oceanwith a realistic nonlinear equation of state. The most general such expressionis the `inactive wind' solution, an exact nonlinear solution of the inviscidcompressible Navier-Stokes that satisfies the continuity equation as aconsequence of Ertel's potential vorticity theorem. Such expressions are shownto be non-unique due to the non-uniqueness of the choice of Bernoulli functionand in general approximately differ by the magnitude of their vertical velocitycomponent. Due to the thermobaric nonlinearity of the equation of state, theexpression of the 3D velocity field for a compressible ocean is found toresemble its ideal fluid counterpart only if constructed in terms of theavailable form of Bernoulli function as per Lorenz theory of availablepotential energy (APE). APE theory also naturally defines a quasi-materialapproximately neutral density variable called Lorenz reference density, whichin turn defines a potential vorticity variable minimally affected bythermobaric production, thus providing all necessary tools for extending mostresults of ideal fluid thermocline theory to a compressible ocean.

On the determination of the 3D velocity field in terms of conserved variables in a compressible ocean