JP1.9
The rotating Green-Naghdi shallow water model: a simple framework for the investigation of mesoscale atmospheric and oceanic flows
Joseph Daniel Pearce, University College, London, London, United Kingdom; and J. G. Esler
There is a long history in geophysical fluid dynamics
of the use of the rotating shallow water equations (rSWE)
to model and understand a wide range of observed phenomena in the atmosphere
and oceans. However, the rSWE have the well-known property that
finite-amplitude gravity waves have a strong tendency to steepen and break.
In many observed mesoscale phenomena, by contrast, wave steepening is opposed
by dispersive
effects, often leading to the formation of stable
nonlinear (e.g. solitary) waves.
The Green-Naghdi (GN) equations are an extended shallow water set with many
appealing properties, such as the parcel-wise
conservation of a potential vorticity, which include dispersive effects and
consequently support stable nonlinear gravity wave motion including solitary
waves.
Here a new pseudo-spectral algorithm is introduced to solve the GN equations
numerically on a doubly periodic f-plane. The following questions,
concerning
the interaction of nonlinear gravity waves and balanced motion,
are then investigated: to what extent do solitary waves and vortices interact?
what happens when the Froude number locally exceeds unity in an initially
`balanced' flow? what controls the generation of nonlinear waves
during transcritical flow (Froude number near unity) over an obstacle of finite
height? It is argued that the rotating GN equations are the simplest set
to allow the above class of problems to be addressed.
Joint Poster Session 1, Theory
Monday, 8 June 2009, 4:30 PM-6:00 PM, Stowe Room
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