TY - JOUR
T1 - A Conservative Model for Nonlinear Dynamics in a Stratified, Rotating Fluid
A1 - Filatoff,Nicolas
A1 - Carton,Xavier
AD - Ad Optimum Company, Paris, France
AD - (UBO/LOPS), Brest, France
UR - https://archimer.ifremer.fr/doc/00600/71195/
DO - 10.4236/ojms.2018.82013
KW - Incompressible and Stratified Fluids
KW - Intermediate Model
KW - Rossby Number
KW - Burger Number
KW - Conservation Properties
KW - Energy
KW - Potential Vorticity
N2 - 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.
Y1 - 2018
PB - Scientific Research Publishing, Inc,
JF - Open Journal of Marine Science
SN - 2161-7384
VL - 08
IS - 02
SP - 253
EP - 275
ID - 71195
ER -