A Laboratory Study of the Zonal Structure of Western Boundary Currents

Abstract

The zonal structure of strongly nonlinear inertial western boundary currents (WBCs) is studied experimentally along a straight "meridional" coast in a 5-m-diameter rotating basin by analyzing the "zonal" profile of the meridional velocity field as a function of transport intensity and other dynamical parameters. The return flow that is generated by the surface wind stress curl in the oceanic interior is forced in the rotating basin by the motion of a piston, in the absence of any surface stress. The laboratory setup consists of two parallel rectangular channels separated by an island and linked by two curved connections: in the first channel, a piston is forced at a constant speed u p ranging from 0.5 to 3 cm s Ϫ1 over a distance of 2.5 m, producing a virtually unsheared current at the entrance of the second channel. In the latter, a linear reduction of the water depth provides the topographic beta effect that is necessary for the development of the westward intensification. Nearly steady currents are obtained and measured photogrammetrically over a region of about 1 m 2 . In all of the experiments performed, an appropriate horizontal Reynolds number (Re ϭ /E, where and E are dimensionless numbers measuring the importance of nonlinearity and lateral friction, respectively) is Re k 1. The zonal profile of the meridional velocity is always found to have (away from the viscous boundary layer) a nearly exponential structure typical of inertial WBCs, whose width agrees well with the classical inertial boundary layer length scale ␦ I . A control experiment (with u p ϭ 1 cm s Ϫ1 ) is analyzed in detail: it has the same as the Gulf Stream (GS) but a much smaller E. This implies that the laboratory flow is expected to be geometrically similar to the GS outside the viscous boundary layer, but to differ within it. To assess the effect of such a departure from dynamic similarity, a mathematical model is used that numerically simulates a flow that is fully dynamically similar to the GS. The comparison between the profile thus obtained numerically and the one obtained experimentally shows that they are, indeed, virtually coincident outside the viscous boundary layer, except for a small offset that tends to vanish as Re → ϱ. Moreover, additional sensitivity experiments in which the piston speed, the rotation rate of the basin, the topographic beta effect, and the width of the main channel are varied provide further information on the zonal structure of WBCs.

Laboratory experiments reveal intrinsic self-sustained oscillations in ocean relevant rotating fluid flows

“…The experiments carried out in the present laboratory study lie in the same inertial regime obtained in 49,50 , but even stronger nonlinear effects are attained over a long duration thanks to the new pumping system (see the discussion in the preceding subsection). This has allowed us to explore a wider range of nonlinear WBC intensity, so that the transitions to time-dependent flows could be investigated.…”

“…This has motivated the 19GAPWEB-HYDRALAB+ project, which was carried out with the 13-m-diameter Coriolis-LEGI rotating platform. The experimental setup was based on a substantial extension of three previous laboratory experiments performed by Pierini et al 40 with the old Coriolis rotating tank of CNRS-Grenoble and by Pierini et al 49,50 with the 5-m diameter Coriolis rotating tank of SINTEF in Trondheim (Norway).…”

“…In the real ocean, the vorticity input is provided by an anticyclonic wind system, but the only way to mimic it in a rotating tank experiment is to apply a rotating rigid lid over the water surface 38 : this is not feasible with large rotating platforms, so a remote mechanical control was adopted in 49,50 , and the same is done here. Moreover, the use of a two-layer fluid would be necessary to account for baroclinic effects, but an inclined rigid lid would be required to impart the beta effect to the upper layer 48 : again, since a rigid lid cannot be introduced in our case, homogeneous water was used.…”

“…It must be stressed that, apart from the new fundamental feature constituted by the lateral gap, there is another very important difference with respect to the setup first introduced in 49 and later applied in 50 : the flow inside the channel C, that was generated by a moving paddle in the previous experiments, is now produced by a pumping system. The great advantage lies in the possibility of performing experiments with almost unlimited duration, while the duration with the moving paddle was limited by the time the latter reached its southernmost limit.…”

“…To study the dynamic similarity between the laboratory experiments and the full-scale ocean phenomena one can rely on the evolution equation of potential vorticity in the quasigeostrophic approximation 1 (valid for our experiments because the Rossby number for a typical simulated WBC is much less than unity) in its steady and dimensionless form 49 . In such equation three dimensionless parameters, ε , E and F, appear measuring the importance of nonlinear inertial effects and that of lateral and bottom friction, respectively 49,50 .…”