52
In (b), KuM2 = qlSuM2, appearing in the production terms of (18) and (19), is computed with
the help of the quasi-equilibrium version of Su o In (c), it is K/Ju/i)z = qlSui)u/i)z that is
evaluated by resorting to the modified stability function Su' as defined in (21) . The quasiequilibrium closure is used in the run (d).
Vai.t treq, N (10-1 .-1)
(b)
V.t... freq. 111 (10 -1 , -I )
2
I
•
!
" .
. j ] . •..
.!!
" '0 •
•
,".
o. II .
1.
1.
2 .
1.
!
~
j 1I.'
H .O
:5
c • . •
4' .'
I
.. ..
o. II .
.. ..
'0 .
buoJ"IU.C!J b (10. ' m .-f)
buoyanc7 b (IO- ~ m -4
Figure 4. Profiles of Brunt-Vruslilli frequency N (solid curves) and buoyancy (= -g(p- po)/po)
(dashed curves) for! = 0 (no rotation) and t = 30 hours in the four types of numerical
simulations.
First, the four types of simulations are carried out with! = 0, a time step of I1t = 120 s, and
a grid size of Ilz = 1 m. When! = 0, laboratory data (Kato and Phillips, 1969), that may be
transposed to marine scales, show that the turbulent layer depth d T may be evaluated, in a very
reliable manner, as d T = (6/5)1/4 u* N o - 1I2 t1(2 (Price, 1979). All simulations are limited to 30
hours, in order not to exceed the domain of validity of Price's formula (1979).
Deleersnijder and Luyten (1994) show that, in the four types of simulation, the thickness of
the turbulent layer is within a few percents of Price's formula (1979). The best agreement is
obtained with the quasi-equilibrium model, but this is not a decisive argument in favour of this
closure scheme, for the discrepancies between the theoretical and predicted values of d are
rather small in all model runs.
In experiment (a), the profiles of velocity (Fig. 3a) and density (Fig. 4a) predicted by the
standard model exhibit a level of noise that is certainly unphysical. The variability of u and p is
associated with large oscillations of the eddy viscosity and the eddy diffusivity (Fig. Sa). The
results of the quasi-equilibrium closure are obviously much better, as depicted in Figs. 3d, 4d,
and 5d.
In (b), KuM2 = qlSuM2, appearing in the production terms of (18) and (19), is computed with
the help of the quasi-equilibrium version of Su o In (c), it is K/Ju/i)z = qlSui)u/i)z that is
evaluated by resorting to the modified stability function Su' as defined in (21) . The quasiequilibrium closure is used in the run (d).
Vai.t treq, N (10-1 .-1)
(b)
V.t... freq. 111 (10 -1 , -I )
2
I
•
!
" .
. j ] . •..
.!!
" '0 •
•
,".
o. II .
1.
1.
2 .
1.
!
~
j 1I.'
H .O
:5
c • . •
4' .'
I
.. ..
o. II .
.. ..
'0 .
buoJ"IU.C!J b (10. ' m .-f)
buoyanc7 b (IO- ~ m -4
Figure 4. Profiles of Brunt-Vruslilli frequency N (solid curves) and buoyancy (= -g(p- po)/po)
(dashed curves) for! = 0 (no rotation) and t = 30 hours in the four types of numerical
simulations.
First, the four types of simulations are carried out with! = 0, a time step of I1t = 120 s, and
a grid size of Ilz = 1 m. When! = 0, laboratory data (Kato and Phillips, 1969), that may be
transposed to marine scales, show that the turbulent layer depth d T may be evaluated, in a very
reliable manner, as d T = (6/5)1/4 u* N o - 1I2 t1(2 (Price, 1979). All simulations are limited to 30
hours, in order not to exceed the domain of validity of Price's formula (1979).
Deleersnijder and Luyten (1994) show that, in the four types of simulation, the thickness of
the turbulent layer is within a few percents of Price's formula (1979). The best agreement is
obtained with the quasi-equilibrium model, but this is not a decisive argument in favour of this
closure scheme, for the discrepancies between the theoretical and predicted values of d are
rather small in all model runs.
In experiment (a), the profiles of velocity (Fig. 3a) and density (Fig. 4a) predicted by the
standard model exhibit a level of noise that is certainly unphysical. The variability of u and p is
associated with large oscillations of the eddy viscosity and the eddy diffusivity (Fig. Sa). The
results of the quasi-equilibrium closure are obviously much better, as depicted in Figs. 3d, 4d,
and 5d.