Adam M. Fincham

Decaying grid turbulence in a strongly stratified fluid

Grid turbulence experiments have been carried out in a stably stratified fluid at moderately large Reynolds numbers (160 based on the Taylor microscale). A scanning particle image velocimetry technique is used to provide time-resolved velocity fields in a relatively large volume. For late times, in the low-Froude-number regime, the flow consists of quasi-horizontal motion in a sea of weak internal gravity waves. In this regime the dynamics of the flow is found to be independent of the ambient stratification. Fundamental differences with two-dimensional turbulence, due to the strong vertical shearing of horizontal velocity, are observed. In this regime, a self-similar scaling law for the energy decay and the length-scale evolution are observed. This behaviour reflects a process of adjustment of the eddy aspect ratio based on a balance between the horizontal advective motion which tends to vertically decorrelate the flow and the dissipation due to the strong vertical shear. The characteristic vertical size of the eddies grows according to a diffusion law and is found to be independent of the turbulence generation. The organization of the flow into horizontal layers of eddies separated by intense shear leads to a strong anisotropy of the dissipation: this has been checked by direct measurement of the different tensorial components of the viscous dissipation.

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.

Decaying grid turbulence in a rotating stratified fluid

Rotating grid turbulence experiments have been carried out in a stably stratified fluid for relatively large Reynolds numbers (mesh Reynolds numbers up to 18000). Under the combined effects of rotation and stratification the flow degenerates into quasihorizontal motions. This regime is investigated using a scanning imaging velocimetry technique which provides time-resolved velocity fields in a volume. The most obvious effect of rotation is the inhibition of the kinetic energy decay, in agreement with the quasi-geostrophic model which predicts the absence of a direct energy cascade, as found in two-dimensional turbulence. In the regime of small Froude and Rossby numbers, the dynamics is found to be non-dissipative and associated with a symmetric and highly intermittent vertical vorticity field, that displays k(h)(-3) energy spectra. For higher Rossby numbers, fundamental differences with the quasi-geostrophic model are found. A significant decay of kinetic energy, which does not depend on the stratification, is observed. Moreover, in this regime, although both cyclones and anticyclones are initially produced, the intense vortices are only cyclones. For late times the flow consists of an assembly of coherent interacting Structures. Under the influence of both rotation and stratification, they take the form of lens-like eddies with aspect ratio proportional to f/N.

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.

The structure and dynamics of dipolar vortices in a stratified fluid

The three-dimensional structure and decay of a dipolar vortex in a linearly stratified fluid is investigated experimentally using a high-resolution three-dimensional scanning correlation image velocimetry system (SCIV). Comparisons with simple theoretical and numerical models are made for late times in the low-Froude-number regime. The relatively well-known stratified dipole, most of the time assumed to be quasi-two-dimensional, is revealed to have a complex three-dimensional vortex topology arising from its self-induced propagation. As the buoyancy scale u/N approaches zero the dynamics of such a structure are dominated by the horizontal velocity field, whereas the diffusion is mainly vertical. The evolution is then governed by an effective Reynolds number, Re eff , based on vertical diffusion and horizontal advection. At early times this effective Reynolds number is large, horizontal advection terms dominate and a decrease of aspect ratio of the structure is observed until Re eff reaches a critical value Re c eff ∼O(1), independent of the initial condition and associated with a horizontal advection-vertical diffusion balance. Thereafter the evolution becomes purely diffusive with decay time Re c eff .

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.