TITLE:
A Conservative Model for Nonlinear Dynamics in a Stratified, Rotating Fluid
AUTHORS:
Nicolas Filatoff, Xavier Carton
KEYWORDS:
Incompressible and Stratified Fluids, Intermediate Model, Rossby Number, Burger Number, Conservation Properties, Energy, Potential Vorticity
JOURNAL NAME:
Open Journal of Marine Science,
Vol.8 No.2,
April
3,
2018
ABSTRACT: We present a set of equations describing the nonlinear dynamics of flows
constrained by environmental rotation and stratification (Rossby numbers Ro∈[0.1,0.5] and Burger numbers of order unity). The fluid is assumed
incompressible, adiabatic, inviscid and in hydrostatic balance. This set of
equations is derived from the Navier Stokes equations (with the above
properties), using a Rossby number expansion with second order truncation.
The resulting model has the following properties: 1) it can represent motions
with moderate Rossby numbers and a Burger number of order unity; 2) it
filters inertia-gravity waves by assuming that the divergence of horizontal
velocity remains small; 3) it is written in terms of a single function of space
and time (pressure, generalized streamfunction or Bernoulli function); 4) it
conserves total (Ertel) vorticity in a Lagrangian form, and its quadratic norm
(potential enstrophy) at the model order in Rossby number; 5) it also
conserves total energy at the same order if the work of pressure forces
vanishes when integrated over the fluid domain. The layerwise version of the
model is finally presented, written in terms of pressure. Integral properties
(energy, enstrophy) are conserved by these layerwise equations. The model
equations agree with the generalized geostrophy equations in the appropriate
parameter regime. Application to vortex dynamics are mentioned.