Etudes et évaluation de processus océaniques par des hiérarchies ...
Etudes et évaluation de processus océaniques par des hiérarchies ... Etudes et évaluation de processus océaniques par des hiérarchies ...
100 CHAPITRE 4. ETUDES DE PROCESSUS OCÉANOGRAPHIQUES A. Wirth, B. Barnier / Ocean Modelling 12 (2006) 101–111 109 tel-00545911, version 1 - 13 Dec 2010 velocity, except for the case with no rotation and the equatorial case. The magnitude of the velocity is also in good agreement with Eq. (6). Deviations from the constant velocity regime are also observed some 300 m before the plume reaches the floor, a length scale that corresponds to the horizontal dimension of the plume. This comes at no surprise as in flows dominated by rotation, the variation of the velocity vector along the axis of rotation is inhibited (Taylor–Proudman theorem). In Fig. 5(b) the displacement of the plume is divided by the sine of the latitude and it is clearly visible that the renormalized vertical velocity agrees for all three cases considered. Based on this findings we can thus extent the formula (6) of Maxworthy and Narimousa (1994) to cases of tilted convection and obtain: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p w ¼ ffiffiffiffiffiffiffiffi B sinðhÞ 3 B=f sinðhÞ ¼ ð7Þ f ? where f = 2X, f ? ¼ 2X sinðhÞ. The best fit for the normalized velocities gives w(h = 90°) = 2.25 · 10 2 m/s. The plume dynamics at the equator (EQ) is different from all other cases in many aspects. No coherent plume is formed the heavy water sinks and spirals around the horizontal axis of rotation extending in the north–south direction. The extension in this direction is not inhibited as the vertical component of the rotation vector vanishes. No coherent plume speed can be obtained in this case. Another important point is the increased mixing in tilted convection already mentioned in Sheremet (2004). Fig. 1(c)–(e) show indeed smaller size features than Fig. 1(b) which shows a single coherent axis-symmetric structure. In the case of tilted convection the axis-symmetry is broken and the plume evolves in a more chaotic way. The presence of the fine structures as for example thin ‘‘Taylor ink walls’’ in the cases LS and GL increase the mixing as compared to the NP or NR case. The horizontally averaged temperature one-and-a-half days into the convection experiment are shown in Fig. 6. It can be clearly seen that in the experiments involving a vertical and a depth (m) 0 -500 -1000 -1500 -2000 -2500 -3000 -0.0002 -0.0001 0 Average Temp. (K) Fig. 6. Horizontally averaged temperature 1.5 days into the experiment: (—) NP, ( ) LS, (- - -) GL, (– Æ –) NR and (– Æ Æ –) EQ.
4.4. TILTED CONVECTIVE PLUMES IN NUMERICAL EXPERIMENTS 101 110 A. Wirth, B. Barnier / Ocean Modelling 12 (2006) 101–111 horizontal component of the rotation axis the mean temperature at each level is decreased (more negative temperature!) after the passage of the plume head as compared to the case with a vertical axis of rotation, the average temperature in the NR and NP cases is only about half of the value in the LS and GL cases. In the case corresponding to the Labrador Sea and the Golf of Lions the water column above the tip of the front is almost perfectly homogenized. 4. Conclusions and perspectives tel-00545911, version 1 - 13 Dec 2010 Based on direct numerical simulations, we have demonstrated that the horizontal component of the rotation vector has significant qualitative and quantitative consequences on the dynamics of a single convective plume at time scales longer than about a quarter of a day. Our here presented numerical calculations are in close agreement with laboratory experiments of Sheremet (2004). The convection is composed of a sinking in the direction of buoyancy force combined with a stretching along the axis of rotation. The vertical speed of the plume is reduced by the horizontal component of the rotation, and the mixing is increased. We furthermore extent an existing formula for the vertical plume speed in the case of aligned gravity and rotation vectors to the case of an arbitrary angle. The here presented case was restricted to the dynamics of a single plume in an isothermal ocean leading to deterministic convection laws. At convection sites stratification is generally weak as the the water masses are well mixed by previously occurred convection events and, as the restratification process is slow (seasonal time scale). The analysis of the important case of convection by an ensemble of plumes in an isothermal and stably stratified ocean is of stochastic nature. Such investigation, possibly leading to improved parameterizations of open-ocean convection, is presently in progress. An improved parameterization of convection in the Greenland Sea (75° N), Labrador Sea (60° N) and the Golf of Lions (45° N), including ‘‘non-traditional’’ effects, is likely a key to improving hydrostatic ocean global circulation models (OGCMs), especially when problems on climate time scales are considered. Acknowledgments We are grateful to T. Gerkema, Y. Morel, T. Penduff and C. Staquet for discussions. Help from P. Begou with using the visualisation software is highly appreciated. The work was funded by EPSHOM-UJF No. 00.87.070.00.470.29.25. Calculations were performed at IDRIS (project 40727), France. References Busse, F.H., Hartung, G., Jaletzky, M., Sommermann, G., 1998. Experiments on thermal convection in rotating systems motivated by planetary problems. Dyn. Atmos. Oceans 27, 161–174. Fernando, H.J.S., Clien, R.-r., Ayotte, A., 1998. Development of a point plume in the presence of background rotation. Phys. Fluids 10, 2369–2383.
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4.4. TILTED CONVECTIVE PLUMES IN NUMERICAL EXPERIMENTS 101<br />
110 A. Wirth, B. Barnier / Ocean Mo<strong>de</strong>lling 12 (2006) 101–111<br />
horizontal component of the rotation axis the mean temperature at each level is <strong>de</strong>creased (more<br />
negative temperature!) after the passage of the plume head as com<strong>par</strong>ed to the case with a vertical<br />
axis of rotation, the average temperature in the NR and NP cases is only about half of the value in<br />
the LS and GL cases. In the case corresponding to the Labrador Sea and the Golf of Lions the<br />
water column above the tip of the front is almost perfectly homogenized.<br />
4. Conclusions and perspectives<br />
tel-00545911, version 1 - 13 Dec 2010<br />
Based on direct numerical simulations, we have <strong>de</strong>monstrated that the horizontal component of<br />
the rotation vector has significant qualitative and quantitative consequences on the dynamics of a<br />
single convective plume at time scales longer than about a quarter of a day. Our here presented<br />
numerical calculations are in close agreement with laboratory experiments of Sherem<strong>et</strong> (2004).<br />
The convection is composed of a sinking in the direction of buoyancy force combined with a<br />
str<strong>et</strong>ching along the axis of rotation. The vertical speed of the plume is reduced by the horizontal<br />
component of the rotation, and the mixing is increased. We furthermore extent an existing formula<br />
for the vertical plume speed in the case of aligned gravity and rotation vectors to the case<br />
of an arbitrary angle.<br />
The here presented case was restricted to the dynamics of a single plume in an isothermal ocean<br />
leading to d<strong>et</strong>erministic convection laws. At convection sites stratification is generally weak as the<br />
the water masses are well mixed by previously occurred convection events and, as the restratification<br />
process is slow (seasonal time scale). The analysis of the important case of convection by an<br />
ensemble of plumes in an isothermal and stably stratified ocean is of stochastic nature. Such investigation,<br />
possibly leading to improved <strong>par</strong>am<strong>et</strong>erizations of open-ocean convection, is presently in<br />
progress. An improved <strong>par</strong>am<strong>et</strong>erization of convection in the Greenland Sea (75° N), Labrador<br />
Sea (60° N) and the Golf of Lions (45° N), including ‘‘non-traditional’’ effects, is likely a key<br />
to improving hydrostatic ocean global circulation mo<strong>de</strong>ls (OGCMs), especially when problems<br />
on climate time scales are consi<strong>de</strong>red.<br />
Acknowledgments<br />
We are grateful to T. Gerkema, Y. Morel, T. Penduff and C. Staqu<strong>et</strong> for discussions. Help from<br />
P. Begou with using the visualisation software is highly appreciated. The work was fun<strong>de</strong>d by<br />
EPSHOM-UJF No. 00.87.070.00.470.29.25. Calculations were performed at IDRIS (project<br />
40727), France.<br />
References<br />
Busse, F.H., Hartung, G., Jal<strong>et</strong>zky, M., Sommermann, G., 1998. Experiments on thermal convection in rotating<br />
systems motivated by plan<strong>et</strong>ary problems. Dyn. Atmos. Oceans 27, 161–174.<br />
Fernando, H.J.S., Clien, R.-r., Ayotte, A., 1998. Development of a point plume in the presence of background rotation.<br />
Phys. Fluids 10, 2369–2383.
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