Dominique Renouard

Experimental study of the stability of an intermediate current and its interaction with a cape

Abstract To study the behaviour of an intermediate current and its interaction with a cape, a large number of experiments are conducted in the 13 m diameter LEGI «Coriolis» rotating tank. The intermediate current is introduced at its equilibrium level into a stratified fluid initially at rest in solid body rotation. The density and the volume flow rate of the current, as well as the total volume of water in the tank are kept constant during each experiment. We checked that the flow is effectively in geostrophic balance and that the geometric aspect ratios have little or no influence. The flow regime is highly deterministic and is parameterised by the initial (injector) values of the Rossby (or Burger) and Ekman numbers. We observe five typical flow regimes: (1) a stable current for large Rossby and Ekman number, (2) when these parameters decrease the still stable upstream current starts to produce a series of cyclonic vortices attached to the outer edge of the current, (3) further decreasing the controlling parameters leads to an anticyclonic vortex which remains attached to the current, (4) further decrease generates dipoles that shed perpendicularly from the current, and (5) for the smallest values of Rossby and Ekman numbers, we observe the generation of anticyclonic lenses of intermediate water, like “Meddies”. When a cape is introduced along the vertical wall, the most striking result is that stable upstream conditions never lead to lens generation at the cape whereas, when the upstream current is itself unstable, the cape is a privileged place for lens generation, but not the only one. When the current is accompanied by edge cyclones, there is still an anticyclone generated downstream of the cape. The formation rate, lens diameter and spin-up time of the detached lenses are consistent with recent oceanic observations near Cape Saint Vincent (Portugal), where the outflow of Mediterranean water occasionally generates Meddies.

Preliminary results about the stability of an intermediate water current

Abstract Experiments were run on a 14 m diameter rotating platform to study the stability conditions for a constant volume flow rate current of intermediate water. The flow was introduced in a two-layer system initially at rest in solid body rotation, along the sidewall of the tank, and allowed freely to evolve. A sink collected the intermediate water and thus ensured that the free surface height was constant. Thus the upstream conditions were the rotation rate, the volume flow rate, the density and the initial width of the intermediate current, which was in geostrophic equilibrium when it left the source; i.e. its thickness along the wall at the source was fixed by this condition. The relevant parameters appear to be the Ekman and the Burger numbers. The data collected from the experiments are very consistent, and it appears that there were five typical flow regimes: (1) a stable current along the whole basin; (2) a series of cyclonic vortices attached to the outer edge of the current, with an upstream stable current; (3) a large cyclonic vortex attached to an anticyclonic instability; (4) dipoles shed from the current into the interior fluid; and (5) generation of lenses of intermediate water, similar to meddies. This last result shows that no topographical effect is required to generate such long-lived lenses, which then drift slowly upstream as the dipoles do.

Experiments on waves trapped over the continental slope and shelf in a continuously stratified rotating ocean, and their incidence on a canyon

Continental margins form a waveguide for topographic Rossby waves, which can be trapped to the bottom by continuous stratification and concentrated over the continental slope while propagating along the coast. We present results of laboratory wave simulations designed to keep as many dimensionless numbers (Rossby, Burger, normalized frequency, wave steepness, geometrical, Ekman, and Reynolds) as possible similar to those of coastal-trapped waves, such as are observed in coastal regions around the world. The 13-m diameter rotating tank is salt-stratified and a continental slope joins a shallow shelf region along the outer tank circumference to a deep central region. The velocity field is measured using a correlation-based digital particle image velocimetry technique at several depths. Current ellipses downstream from subinertial forcing indicate along-isobath propagation with energy concentrated at depth and three-dimensional structure in agreement with a numerical wave solution calculated using the experimental geometry, rotation rate, and buoyancy frequency. Contrasting the inviscid wave solution, experimental flow shows an asymmetry with positive time-mean uv correlations (u across isobaths toward deep water, v along isobaths with shallow water to the left), and phase variations perpendicular to isobaths with flow near the shelf break leading that farther inshore and offshore, Both of these attributes have been seen previously in ocean observations and are interpreted as the signature of frictional influences based on stratified slope-Kelvin wave behavior. When incident on a canyon that indents the slope and shelf, a wave propagates in to and out of it along isobaths while remaining concentrated over the sloping topography with only weakly modified amplitude and phase structure. Based on the limited range of parameter space studied, the implication is that alongshore wave propagation will remain largely unmodified by natural corrugations in the slope and shelf and loss of energy by scattering will be weak.

Baroclinic wave generation by barotropic waves passing over a shelf

In a 10×2×0.6 m channel we studied baroclinic wave generation by barotropic periodic waves passing over a shelf. Firstly, for fixed experimental conditions, we varied the period, and noticed: 1. (1) that the Froude number defined by F=UsbC2s is suited tharacterize the flow near the edge of the shelf (Usb is the maximum value of the barometric current near the edge of the shelf and C2s is the baroclinic longwave speed over the shelf); 2. (2) that for F<1, the baroclinic wave recorded near the edge of the shelf is quasi-linear and then evolves into non-linear waves as it propagates over the shelf; 3. (3) that, for F>1, the waves are non-linear everywhere. Secondly, for a given period the longitudinal profiles of the interface at various times reveal that: 1. (i) over the slope there is lee-wave formation during part of the period; 2. (ii) when H1<H2s (H1 and H2s upper and lower thickness, respectively), such a wave propagates over the shelf where it evolves to trains of solitary waves of depression; 3. (iii) when H1>H2s, the phenomena are much more complex, but, under some conditions, there may appear trains of solitary waves of elevation over the shelf.

Generation of internal waves over a shelf

Experiments are performed in a 13-m cylindrical tank to study the generation of interfacial internal waves by barotropic sinusoidal waves passing over a slope. At each tidal cycle, there are two waves generated, one propagating onshore and the other propagating offshore. The amplitude of the waves increases with increasing forcing and evolves as nonlinear waves if the shelf width is smaller than the wavelength of the baroclinic tide. Rotation does not modify the generating mechanism but the amplitude of the generated waves decreases with increasing rotation rate; also no internal waves are generated when the forcing period is larger than the inertial period, and at high rotation rate, there are only dispersive waves propagating from the shelf break region. The experiments covered a large range of internal Froude number, Rossby number and temporal Rossby number and compare well with in situ observations.

Two experimental studies of internal waves generated by tide-topography interaction

Abstract Two experiments on the generation of internal waves in a two-layer fluid are considered. In the first experimental configuration, it is shown that when a periodic current flows along a coast and past a cape, dispersive waves are generated to the right of the cape (facing onshore), and trains of rank-ordered solitary Kelvin waves are periodically shed along the wall, to the left of the cape. Moreover, there is a mean current generated in both layers, parallel to the wall, to the left of the cape in the lower layer and to the right of the cape in the upper layer. In the second configuration, it is demonstrated that when a periodic current flows over an obstacle, when the rotation is strong, only dispersive waves can be observed far from the obstacle, whereas when the notation is weak, trains of solitary waves can be observed far from it. The hydraulic conditions over the obstacle affect only the wave amplitude.

Internal waves and rectification in a linearly stratified fluid

Laboratory experiments were performed in a 13-m diameter rotating tank equipped with a continuous shelf break geometry and a central piston-like plunger. The fluid density was linearly stratified. The amplitude and period of the plunger, the rotation rate of the platform and the stratification are the parameters of the problem. The density fluctuations at six stations above and at mid-depth of the slope, along with dye visualization of the flow, were recorded. A limited set of experiments showed that a barotropic periodical forcing generated a first mode baroclinic wave which initially appears at the slope and propagates offshore. The likely presence of internal energy rays either slightly above, or immediately along the slope, is in agreement with previous analytical, laboratory and selected oceanic observations. In the former case, the stratification was such that the slope flow at mid-depth was supercritical while in the latter case, slope flow at mid-depth was critical. Rotation tended to decrease the amplitude of the generated internal wave. Also, non-linear processes were likely to act upon these waves for their normalized amplitude tended to decrease as the forcing increased (for similar forcing period, rotation rate and stratification). After the internal wave reflected from the plunger reaches the slope, there is a complex non-stationary regime with an occurrence of internal wave breaking in the vicinity of the slope. Thus there was an appearance of localized patches of turbulence and mixing. These events appeared both in dye visualization and in density fluctuations records. The subsequent mixing, or else the combined effect of topographical rectification and mixing, led to the appearance of a distinct Lagrangian transport, localized in the first few centimeters above the slope and oriented so as to leave the shallow waters on the right of its displacement.

Experimental study of the reflection of an internal solitary Kelvin wave in a right-angle corner

Abstract Solitary Kelvin waves are made to reflect a right-angle corner. The experiments are performed in a 13 m rotating tank filled with a two-layer system. Kelvin waves were generated by lifting a dam behind which there is a thicker upper-layer. First, by checking that the celerity and shape have the correct amplitude dependence, it is demonstrated that it is possible to generate internal solitary Kelvin waves in a semi-infinite domain, both for weak and strong rotation. Second, we made detailed observations of repeated copies of a low amplitude solitary Kelvin wave reflected by a right-angle corner. There are both (i) a transmitted solitary Kelvin wave propagating along the reflecting wall; and (ii) some Poincare waves radiating from the corner region. There is always a strong decay in amplitude due to the generation of the Poincard waves at the right-angle corner.

Experimental study of the coastal thermocline height variations caused by an impulsively applied wind of limited along-shore extent

Abstract On the large rotating platform of Grenobles University, a channel (8×2×0.6 m) has been built, equipped with a wind entrainment simulation effects mechanism. With a local wind, acting over a two-layered ocean, upwelling or downwelling patterns are induced, which are Kelvin-type height variations of the interface; propagating so that, in the northern hemisphere, they leave the coastline to the right of their direction of propagation, and having a profile exponentially decreasing from the coastline towards the open sea. The agreement between these observations and the recently proposed model of Crepon and Richez (1982) is very good at some distance from the excitation zone. However, this model, for its application, is limited to the situation in which the Ekman layer is of the same order of magnitude as the upper layer. Otherwise the oceanographic observations, as well as our observations, show a cross-shore current in the intermediate layer. Near the boundaries of the excitation zone (i.e., the wind zone), such a current is responsible for vortices which cause local upwelling. The model does not account for such local upwelling which is superimposed on the Kelvin-type height variation of the thermocline. These vortices may be explained by consideration of variations of relative vorticity. The experiments also show that a wind perpendicular to the coast may also induce upwelling or downwelling.

Experimental set up of an Internal wave, Generated by the wind, and of Shorter Period than the Coriolis Period

Abstract In order to study, under laboratory conditions, the generation of internal waves by a suddenly applied wind, taking account of the Coriolis effect, the authors have built on the rotating platform of Grenoble University a large flume (8.0 x 2.0 x 0.6 m) at present equipped with a wind tunnel, but capable of receiving at some future date, a mechanism for simulation of the driving effect of the wind. They first describe the experimental installation and the measuring instruments it supports. Then they submit a theoretical interpretation of the phenomena observed. As a rotating tank is involved, the following are observed: 1) variation in the mean level of the interface; 2) the organization of a Poincare-Kelvin amphidromy; 3) an internal inertial wave, with a shorter period than the inertial period and related to the impulsive character of the wind. Comparison between the experimental results and the theorical forecast reveals the limits of a theory which, at present, does not take account of particularities due to the limited nature of the channel.