Small-scale instabilities of an island wake flow in a rotating shallow-water layer

International audienceUnlike the standard two-dimensional Kármán street, the oceanic vortex streets which may occur behind isolated islands are affected by the earth's rotation and the vertical stratification of the thermocline. These effects induce a selective destabilisation of anticyclonic vorticity regions. Several experimental studies were devoted to the inertial instability, which induces transient and three-dimensional perturbations in a rotating fluid layer. However, these previous experiments correspond to a large or finite vertical h to horizontal L aspect ratio (α=h/L) while in an oceanic context this ratio is much smaller than unity (αsimilar, equals0.01). This vertical confinement induces a cutoff vertical scale for unstable perturbations. But, since dissipation preferentially damps smaller scales, the shallow-water aspect ratio α may become so small that no growth will occur. We present here the first experimental investigation of three-dimensional destabilizations of an island wake flow in a shallow-water configuration. These laboratory experiments where performed on the LEGI Coriolis Platform, with small aspect ratio (α=0.1) and large Reynolds numbers (Re=5000–35,000). We have shown that unstable three-dimensional perturbations occur when the island Rossby number View the MathML source is large enough (Ro>0.8) while the Reynolds number seems to control the duration of this transient instability. Qualitative dye visualisation reveals various types of passive tracer dispersion in the wake. Moreover, according to PIV measurements we have shown that, unlike experiments having large or finite aspect ratio (α≥1), the small-scale perturbations do not significantly reduce the local vorticity inside the unstable anticyclone. Hence, the shallow-water configuration (αmuch less-than1) seems to reduce the intensity and the impact of three-dimensional instabilities in the vortex street. Finally, for high Froude numbers, when the flow becomes supercritical and owing to the generation of large amplitude waves in the wake, the vortex street intensity is strongly reduced

Quantitative laboratory observations of internal wave reflection on ascending slopes

International audienceInternal waves propagate obliquely through a stratified fluid with an angle that is fixed with respect to gravity. Upon reflection on a sloping bed, striking phenomena are expected to occur close to the slope. We present here laboratory observations at moderately large Reynolds number. A particle image velocimetry (PIV) technique is used to provide time resolved velocity fields in large volumes. The generation of the second and third harmonic frequencies are clearly demonstrated in the impact zone. The mechanism for nonlinear wavelength selection is also discussed. Evanescent waves with frequency larger than the Brunt-Väisälä frequency are detected and experimental results agree very well with theoretical predictions. The amplitude of the different harmonics after reflection are also obtained

Inertial instability of von Karman street in a rotating shallow-water layer

The rotation alters the stability of 2D anticyclonic flow with respect to 3D perturbations. Experiments have shown that such instability induces a transient destabilization of anticyclonic vortices in von Kármán street, when w/f 5 000). We have shown that unstable 3D-perturbations occur for large enough Rossby number (Ro > 0.8) while the Reynolds number seems to control the duration of this transient instability. According to PIV measurements we have shown that, unlike the deepwater configuration, the small-scale perturbations do not reduce the local vorticity inside the unstable antiyclone. Finally, for high Rossby numbers, when the flow becomes supercritical (Fd > 1), due to the generation of high amplitude wave wake the vortex street intensity is strongly reduced

Impact of dissipation on the energy spectrum of experimental turbulence of gravity surface waves

We discuss the impact of dissipation on the development of the energy spectrum in wave turbulence of gravity surface waves with emphasis on the effect of surface contamination. We performed experiments in the Coriolis facility which is a 13-m diameter wave tank. We took care of cleaning surface contamination as well as possible considering that the surface of water exceeds 100~m$^2$. We observe that for the cleanest condition the frequency energy spectrum shows a power law decay extending up to the gravity capillary crossover (14 Hz) with a spectral exponent that is increasing with the forcing strength and decaying with surface contamination. Although slightly higher than reported previously in the literature, the exponent for the cleanest water remains significantly below the prediction from the Weak Turbulence Theory. By discussing length and time scales, we show that weak turbulence cannot be expected at frequencies above 3 Hz. We observe with a stereoscopic reconstruction technique that the increase with the forcing strength of energy spectrum beyond 3~Hz is mostly due to the formation and strenghtening of bound waves.Comment: accepted for publication in Physical Review Fluid

From internal waves to turbulence in a stably stratified fluid

We report on the statistical analysis of stratified turbulence forced by large-scale waves. The setup mimics some features of the tidal forcing of turbulence in the ocean interior at submesoscales. Our experiments are performed in the large-scale Coriolis facility in Grenoble which is 13 m in diameter and 1 m deep. Four wavemakers excite large scale waves of moderate amplitude. In addition to weak internal wave turbulence at large scales, we observe strongly nonlinear waves, the breaking of which triggers intermittently strong turbulence at small scales. A transition to strongly nonlinear turbulence is observed at smaller scales. Our measurements are reminiscent of oceanic observations. Despite similarities with the empirical Garrett & Munk spectrum that assumes weak wave turbulence, our observed energy spectra are rather be attributed to strongly nonlinear internal waves.Comment: accepted for publication in Physical Review Letter

Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility

We investigate experimentally stratified turbulence forced by waves. Stratified turbulence is present in oceans and it is expected to be dominated by nonlinear interaction of internal gravity waves as described by the Garrett & Munk spectrum. In order to reach turbulent regimes dominated by stratification we use the Coriolis facility in Grenoble (France) which large size enables us to reach regimes with both low Froude number and large Reynolds number. Stratification is obtained by using vertically linearly varying salt concentration and we force large scale waves in a $6\times6\times 1$ m$^3$ domain. We perform time-resolved PIV to probe the space-time structure of the velocity field. We observe a wide band spectrum which is made of waves. Discrete modes are observed due to the square shape of the flow container as well as a continuum part which appears consistent with an axisymmetric superposition of random weakly nonlinear waves. Our observations support the interpretation of turbulence of a strongly stratified fluid as wave turbulence of internal waves although our spectrum is quite different from the Garrett & Munk spectrum. Weak turbulence proceeds down to a small cutoff length scale (the buoyancy wavelength) at which a transition to more strongly nonlinear turbulence is expected.Comment: accepted for publication in Physical Review Fluid