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 Effect of the rotation on the discretization of a square domain.
 Effect of a poor resolution on the geometry of a strait.
 Elevation field for the Kelvin retardation problem in presence of steps
along the walls at two different resolutions.
 The three major horizontal staggerings for
the primitive equations.
 Triangulation of the domain.
 ,
the basis function related to the node M_{i}.

is the basis function related to the node x_{2}=0.
 The discontinuous linear non conforming basis function for
the
P_{1}^{NC}P_{1} element of Hua and Thomasset hua84.
 The discontinuous constant basis function for pressure
over the macroelement of LLS.
 Local nonorthogonal coordinates in a given triangle
 Example of Legendre polynomials
 Remeshing strategies. The triangle to be refined is in grey.
 Transformation of one triangle intro a curved triangle
 Transformation of one triangle intro a curved triangle with
the coordinate system used in the computation of the
integrals
 The wave test experiment
 Convergence with resolution of the
normalized error in the ucomponent for second order Cgrid formulation
(FDM), OFDM4 and RFDM4 models.
 CPU cost with the normalized error in ucomponent
for the second order Cgrid
(FDM) and RFDM4 models.
 The four FE models (LW, HT, PZM, LLS) are tested against the
analytical solution with increasing resolution.
 Convergence of the normalized error in
v with respect to the resolution for the LWFE
and SE models
 Convergence of the normalized error in u with
respect to the resolution
for the Cgrid FD, LWFE
and SE models.
 Variation in the ucomponent normalized error as a function of CPU cost for
five models.
 Grids for the circular domain for the FD models.
 Convergence with resolution of the
normalized elevation error for the second order Cgrid FD,
OFDM4 and RFDM4 models in a circular domain.
 Elevation error in a circular domain for four FE models.
 Normalized elevation error for the Cgrid FD, LWFE and
SE models for a circular domain.
 Total energy after 18 days of simulation for the
Cgrid FD and the lumped LW, delumped LW, PZM and LLS FE models
and the SE model for the geostrophically balanced
eddy.
 Elevation field after a six year simulation in a nonrotated
basin using OFDM4 and RFDM4.
 As for Figure 3.13 but for rotated basin.
 Kinetic energy during a 6 year spinup for the
Cgrid FD, the lumped LW, HT, PZM and LLS
FE models.
 Elevation field after a 6 year spinup for the
Cgrid FD, the lumped LW, delumped LW,
HT, PZM and LLS FE models for the single gyre wind
forcing problem.
 Single gyre wind forcing experiments for the delumped LW FE model
compared to the Cgrid FD model.
 Kinetic energy during spinup for the
single gyre Munk problem with
m^{2}s^{1} for
the Cgrid FD, the delumped LW FE and SE models.
 Elevation field for the SE model after 6 years from spinup for the
single gyre Munk problem with
m^{2}s^{1},
n_{c}=5.
 As for Fig. 3.18
but with
m^{2}s^{1}.
 As for Fig. 3.19
but with
m^{2}s^{1}.
 Convergence with resolution for the nonlinear Munk problem
of the normalized kinetic energy error for the solution
from the Cgrid FD and the SE models.
 As for Fig. 3.22 but for the
convergence of the normalized error with CPU cost.
 Solutions after a 6 year spinup for the Munk problem using the
adaptive SE model with n_{c}=5.
 Locations of variables near a step for the SW Cgrid
model and the QG model.
 Local advective flux along the boundary at 20 km
resolution in a square basin for the enstrophy conserving
formulation.
 Northward flow past a forward step.
The shaded area is the model domain.
 Elevation fields in meters after a 6 year spinup for 20 km and 10 km
resolution. Shown are results from the A and B combination with or without
a 3.44^{o} rotation angle of the basin.
 (a) Kinetic energy after spinup and (b)
ratio of
to
for the four combinations
combinations.

Kinetic energy after spinup for the B combination in
10^{10} m^{5}/s^{2}.
 Ratio of
to
for the B combination.

Convergence of
with
resolution for 0^{o}, 20^{o}, 45^{o} rotation angle
for the B combination.
 Kinetic energy during spinup for six runs
using the J_{1} Jacobian at 6 different rotation angles.

Kinetic energy after spinup for
(a) J_{3} at 0^{o} rotation,
(b) J_{7} at 0^{o},
(c) J_{3} at 30^{o},
(d) J_{7} at 30^{o},
(e) J_{3} at 30^{o},
(f) J_{7} at 30^{o}.
 Ratio of
to the wind input for
(a) J_{3} at 0^{o} rotation,
(b) J_{7} at 0^{o},
(c) J_{3} at 30^{o},
(d) J_{7} at 30^{o}.
 Ratio of
to the wind input. (ad) as
described in Fig. 4.10.

Ratio of
to the wind input. (ad) as
described in Fig. 4.10.
 Semiadvective flux, <
, and beta contribution,
, to the
vorticity budget for the J_{3} Jacobian at 30^{o} rotation angle.
 Notation corresponding to the curvilinear coordinates.
 The five geometries used for our application of the SE method.
 Elevation fields in the Geometry V for the Cgrid model
after 3 years of spinup.
 Total energy during spinup for the A and B combinations of the FD
Cgrid model and for the SE model at n_{c}=5 (SPOC 5) in Geometry V.
m^{2}s^{1}.
 Mean elevation fields for the five geometries using the SE model.
 Mean vorticity field for the Geometries IV and V using the SE
model.
 Power input by the wind using the mean fields with respect to the
boundary Reynolds number.
 Mean standard deviation of the elevation.
 Mean standard deviation of the elevation for frequencies with
period above 200 days.
 Mean standard deviation of the elevation for frequencies with
period between 17 and 200 days.
 Mean standard deviation of the elevation for frequencies with
period between .6 and 17 days.
 Hovmöller diagram of the filtered elevation with respect to
time and location along the boundary.
 Amplitude of the Kelvin wave in meters along the boundary averaged
over 6 years.
 Time series of the amplitude of the oscillations at (x=500 km, y=0
km).
 Total energy for the last 6 years of simulation.
 Instantaneous vorticity field in the vicinity of the recirculation.
 (a) Local wind input to the vorticity in Geometry V.
(b) Local divergence of the eddy
transport of vorticity in Geometry V.
(c) Vector plot of the eddy transport of vorticity normal to the
streamlines in Geometry V.
 The region in grey represents where the absolute vorticity is
approximately conserved.
 Maximum of the mean elevation for the three geometries. The
maximum elevation is a good proxy for the strength of the recirculation.
 Kinetic energy of the mean fields with respect to the boundary
Reynolds number.
 Mesh for the original and the refined runs.
 Total energy for the last 6 years of simulation for the original
and refined meshes.
 Amplitude of the fast oscillations at (x=500 km, y=0 km) along the
boundary for the original and refined meshes.
 Mean elevation fields for the original mesh and the refined mesh.
 Mean vorticity fields for the original mesh and the refined mesh.
Frederic Dupont
20010911