Henri Didelle

Dynamics of Convectively Driven Banded Jets in the Laboratory

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “ effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s 1 . Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (/Urms) 1/2 . This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k 5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

A novel internal waves generator

We present a new kind of generator of internal waves which has been designed for three purposes. First, the oscillating boundary conditions force the fluid particles to travel in the preferred direction of the wave ray, hence reducing the mixing due to forcing. Second, only one ray tube is produced so that all of the energy is in the beam of interest. Third, temporal and spatial frequency studies emphasize the high quality for temporal and spatial monochromaticity of the emitted beam. The greatest strength of this technique is therefore the ability to produce a large monochromatic and unidirectional beam.

Experiments with density currents on a sloping bottom in a rotating fluid

Abstract The behaviour of a density current on a sloping bottom in a rotating system is investigated by laboratory experiments. The main result is that the dense bottom outflow induces cyclonic vortices in the upper fluid layer, which are formed periodically and move to the west parallel to coast. Two regimes of vortex formation have been identified. For strong density currents and weak rotation, vortices are formed by stretching of the upper layer near the source as found also in the experiments by Lane-Serff and Baines (1998) [Lane-Serff, G.F., Baines, P.G., 1998. Eddy formation by dense flows on slopes in a rotating fluid. J. Fluid Mech. 363, 229–253]. For weak density currents and strong rotation vortices are due to instability of the bottom plume itself as found in the numerical simulations of Jiang and Garwood (1996) [Jiang, L., Garwood, W. Jr., 1996. Three-dimensional simulations of overflows on continental slopes. J. Phys. Oceanogr. 26, 1224–1233].

Jupiter's and Saturn's convectively driven banded jets in the laboratory

The banded patterns of cloud and wind are among the most striking features of the atmospheres of Jupiter and Saturn, but their dynamical origin remains poorly understood. Most approaches towards understanding zonation so far (also in the terrestrial oceans) have used highly idealized models to show that it might originate from dynamical anisotropy in a shallow turbulent fluid layer due to the planetary β-effect. Here we report the results of laboratory experiments, conducted on a 14-m diameter turntable, which quantitatively confirm that multiple zonal jets may indeed be generated and maintained by this mechanism in the presence of deep convection and a topographic β-effect. At the very small values of Ekman number (≤2 × 10−5) and large local Reynolds numbers (≥2000, based on jet scales) achieved, the kinetic energy spectra suggest the presence of both energy-cascading and enstrophy-cascading inertial ranges in addition to the zonation near twice the Rhines wave number.

Quantitative laboratory observations of internal wave reflection on ascending slopes

Internal 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 technique is used to provide time-resolved velocity fields in large volumes. Generation of the second and third harmonic frequencies is clearly demonstrated in the impact zone. The mechanism for nonlinear wavelength selection is also discussed. Evanescent waves with frequency larger than the Brunt-Vaisala frequency are detected and experimental results agree very well with theoretical predictions. The amplitude of the different harmonics after reflection is also obtained.

A laboratory study of surface boundary currents: Application to the Algerian Current

The problem of a gravity current along a coast is considered in the laboratory. The flow originates from a continuous pointsource and, when facing downstream, has the shore to its right. The shore is the vertical wall of a 13-m-diameter rotating basin. The density of the current, r1, is slightly less than that of the surrounding fluid. This buoyant flow is shown to depend upon three parameters; namely, the Burger and Ekman numbers and the aspect ratio of the current at its source. Disregarding friction and taking the flow as hydrostatic so that the current aspect ratio does not need to be considered, the stability characteristics of the current are shown to depend mostly upon the Burger number. To study its role in the flow, we performed several experiments by varying the Burger number Bu between 0.15 and 0.82. For large Burger numbers the current is stable, but as it decreases, increasing numbers of anticyclonic disturbances develop and grow along the axis of the current. Measurements of the normalized distance from the source, and times for these disturbances to develop, are given as functions of the Burger number. The dependence of the normalized separation distance of disturbances upon the Burger number, in cases of multiple instabilities, is also discussed. Finally, these laboratory results are compared with the Algerian Current, where both anticyclonic and cyclonic eddies have been observed. The experimental current simulates the Algerian Current when the Burger number is 0.15.

A laboratory study of low-mode internal tide scattering by finite-amplitude topography

We present the first laboratory experimental results concerning the scattering of a low-mode internal tide by finite-amplitude Gaussian topography. Experiments performed at the Coriolis Platform in Grenoble used a recently conceived internal wave generator as a means of producing a high-quality mode-1 wave field. The evolution of the wave field in the absence and presence of a Gaussian was studied by performing spatiotemporal modal decompositions of velocity field data obtained using particle image velocimetry. The results support the belief that finite-amplitude topography produces significant reflection of the internal tide and transfer of energy from low to high modes.

Laboratory Simulation of Tidal Rectification over Seamounts: Homogeneous Model

Abstract The problem of the oscillatory motion of a homogeneous, rotating fluid in the vicinity of an isolated topographic feature is investigated in the laboratory and numerically. The laboratory experiments are conducted by fixing a cosine-squared body of revolution near the outer boundary of a circular tank rotating about a vertical axis with an angular velocity Ω(t)=Ω0+Ω1sinωt, where Ω0 is the mean background rotation and Ω0 and ω are the magnitude and frequency of an oscillatory component. Experiments with an oscillatory flow show clearly that a mean anticyclonic vortex is formed in the vicinity of the topographic feature. Surface floats are used to determine typical particle paths for various flow conditions and these are shown to vary markedly with the Rossby and temporal Rossby numbers of the background flow. Eulerian velocity profiles along and normal to the streamwise axis are used to quantify the anticyclonic vortex. A scaling analysis is advanced to show how the strength and distribution of th...

On the formation and shedding of vortices from side-wall mounted obstacles in rotating systems

Abstract The flow of a homogenous, incompressible, rotating (vertically upward) fluid past cylinders of triangular and semi-circular cross-section mounted on either the left or right wall (facing downstream) of a channel is investigated experimentally. The pertinent system parameters are the Rossby and Ekman (or Reynolds) numbers and the obstacle width to fluid depth ratio. The experiments indicate that the shedding of tip eddies from the triangular obstacle leads to a rather complex wake motion which is critically dependent on the system parameters. For certain parameter combinations the tip eddies advect downstream as single entities while in other regions of parameter space two or more eddies merge and advect downstream as large-scale eddy structures. The Strouhal numbers for both the shedding of the tip eddies as well as of the large-scale structures are measured as functions of the system parameters. Measurements of the dimensionless size of the large-scale starting eddies are made as functions of a dimensionless time and other system parameters. It is shown that eddies formed in the lee of obstacles mounted on the right (anticyclonic) tend to shed more quickly, other parameters being fixed, than those on the left (cyclonic). Measurements of the dimensionless vorticity of the cores of the large-scale structures at a fixed dimensionless time indicate that, within the accuracy of the experiments and for the range of parameters considered, this quantity is independent of the Rossby and Reynolds numbers and the side to which the obstacle is mounted. Finally some of the experimental flow patterns are shown to be similar to a recent observation of a southeastward ocean current past the western tip of Grand Bahama Island.

Rectified flow along a vertical coastline

Abstract Laboratory experiments are conducted on a physical system in which an oscillatory, along-shore, free stream flow of a homogeneous fluid occurs in the vicinity of a long coastline with vertical slope; the model sea-floor is horizontal. Particular attention is given to the resulting rectified (mean) current which is along the coastline with the shore on the right, facing downstream. In the lateral far field region defined by y H ⪢ O (1), where y is the offshore coordinate and H is the depth of the fluid, the motion field is approximately independent of the lateral distance from the coast. The vertical structure of the cross-stream motion in this region consists of Ekman layers near the sea-floor and interior adjustment flows, both periodic in time. In the near field, defined by y H ⪅O (1), the motion is strongly dependent on the cross-stream coordinate as well as time, and rectified currents are observed. The mechanism responsible for the rectification is a complex nonlinear coupling between laterally directed adjustment flows driven by the transport in the bottom Ekman layers, and the free stream motion field. The rectified current is found to be substantially wider than the Stewartson layer thickness but much narrower than the Rossby deformation radius. The characteristic width, δ y , of the rectified current is shown to scale as δ y H ∼ RoRo t −1 E 1 2 , where Ro is the Rossby number Ro t is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling.