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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

International audienceThe usual geophysical approximations are reframed within a variational framework. Starting from the Lagrangian of the fully compressible Euler equations expressed in a general curvilinear coordinates system, Hamilton's principle of least action yields Euler-Lagrange equations of motion. Instead of directly making approximations in these equations, the approach followed is that of Hamilton's principle asymptotics; that is, all approximations are performed in the Lagrangian. Using a coordinate system where the geopotential is the third coordinate, diverse approximations are considered. The assumptions and approximations covered are 1) particular shapes of the geopotential; 2) shallowness of the atmosphere, which allows for the approximation of the relative and planetary kinetic energy; 3) small vertical velocities, implying quasi-hydrostatic systems; and 4) pseudoincompressibility, enforced by introducing a Lagangian multiplier. This variational approach greatly facilitates the derivation of the equations and systematically ensures their dynamical consistency. Indeed, the symmetry properties of the approximated Lagrangian imply the conservation of energy, potential vorticity, and momentum. Justification of the equations then relies, as usual, on a proper order-of-magnitude analysis. As an illustrative example, the asymptotic consistency of recently introduced shallow-atmosphere equations with a complete Coriolis force is discussed, suggesting additional corrections to the pressure gradient and gravity

Usual Approximations to the Equations of Atmospheric Motion: A Variational Perspective