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Don L. Boyer
and
Xiuzhang Zhang

Abstract

With the aim of developing increasingly realistic physical models of the interaction of ocean currents with isolated seamounts, laboratory experiments concerning the flow of an oscillatory current past a cosine-squared body of revolution in the presence of background rotation and stratification are considered. The pertinent parameters governing the motion are the Rossby, temporal Rossby, Burger and Ekman numbers, the ratio of the magnitude of the oscillatory velocity component to the mean current and various geometrical parameters. With the exception that the present experiments distort the vertical coordinate, the studies are conducted in regions of parameter space of relevance to the real ocean; future communications will investigate relatively undistorted geometries.

The experiments demonstrate that three fundamentally different flow regimes can be identified and that these are highly sensitive to the value of the Rossby number, Ro. These include, (i) at low Ro a regime in which the flow is fully attached to the obstacle for all phases of the flow cycle, (ii) at moderate Ro a regime in which eddies are attached to the lee side of the topographic feature and, (iii) at high Ro flows in which eddies are shed from the obstacle. Various flow regime diagrams are presented.

Emphasis is given to those aspects of the motion that are related to the unsteady nature of the free stream current. For example, for sufficiently small Rossby numbers, it is shown that fluid parcels advecting over the top of the obstacle exhibit anticyclonic loops similar to those observed recently for diurnal tidal flow past Fieberling Guyot.

Quantitative measures of the size of the leeside bubble region for the attached leeside eddies flow regime, eddy separation distances for the eddy shedding regime, particle residence times for fluid parcels advecting over the topography and upwelling and downwelling measures on the upstream side of the obstacle are presented as functions of the various system parameters.

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Xiuzhang Zhang
and
Don L. Boyer

Abstract

Pure oscillatory flow of a rotating, linearly stratified fluid in the vicinity of an isolated topography of revolution is considered in the laboratory. The pertinent dimensionless parameters governing the motion are the Rossby (Ro), temporal Rossby (Ro t ), Burger (S), and Ekman (E) numbers and geometrical length-scale ratios. Experiments are considered for fixed S, E and geometry and ranges of Ro and Ro t given by 0.003 ≤ Ro ≤ 0.03 and 0.2 ≤ Ro t ≤ 2.4. A Ro t against Ro regime diagram is developed, which includes the following flow classifications: (i) attached flow (AF), (ii) tidal oscillation loops (TOL), (iii) trapped waves-anticyclonic/cyclonic residual current (WAC), (iv) trapped waves-anticyclonic residual current (WA), (v) attached eddies (AE), and (vi) vortex shedding (VS).

For all flow regimes a rectified mean anticyclonic motion is observed in the vicinity of the topography. For superinertial frequencies (i.e., Ro t > 1), a resonance phenomenon enhances the streamwise speed near the obstacle well beyond the corresponding velocity in the undisturbed flow; this flow enhancement is strongest at levels above the summit of the obstacle. The resonance phenomenon, as evidenced by the streamwise and cross-stream sizes of the observed tidal oscillation loops normalized with the undisturbed tidal displacement, is quantified at various streamwise locations for a series of experiments with fixed geometry, Ro=0.013, S=1.0, and various Ro, in the range 0.6≤ Ro t ≤2.4. These experiments demonstrate amplification peaks near Ro t ∼1.0 and 2.0. For subinertial frequencies (i.e., Ro t < 1), the rectified flow is bottom trapped in the sense that the mean anticyclonic flow is strongest near the obstacle and decreases at higher elevations. The laboratory observations are shown to depict some of the qualitative aspects of recent observations of oceanic motions in the vicinity of Fieberling Guyot; in particular, upper-level enhancement of superinertial components and bottom trapping of subinertial ones.

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Xiuzhang Zhang
and
Don L. Boyer

Abstract

A laboratory study has been conducted on the deflection of steady and oscillatory free stream currents impinging on two model seamounts of identical shape. The laboratory model includes the effects of background rotation (f-plane) and stratification (linear). The flows are generated by towing obstacles through a fluid medium that is otherwise at rest with respect to an observer fixed with the rotating frame. The system behavior is investigated as a function of the normalized obstacle separation distance, G = G */D, and angle, θ between the line connecting the obstacle centers and the free-stream direction; here G * is the obstacle center-to-center separation distance and D is the base width of one of the obstacles. The temporal Rossby (for oscillatory cases), Burger, and Ekman numbers and the remaining geometrical parameters are fixed for all of the experiments; characteristic flow variations with the Rossby number, R 0, are investigated.

For the ranges of parameters considered, two characteristic flows are observed with the particular details of the motions depending strongly on G and θ. The first, generally occurring at small R 0, is an attached leeside eddy regime in which eddies are attached to the lee of the topographic features and for which the general flow field is steady. The second, at higher R 0, is an eddy-shedding regime in which eddy structures are periodically formed in the vicinity of the obstacles and shed downstream. Some comments are made on the possible importance of the flow in the vicinity of Fieberling Guyot as it might be affected by its neighbors Fieberling II Seamount and Hoke Guyot.

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Nicolas Perénne
,
Jacques Verron
,
Dominique Renouard
,
Don L. Boyer
, and
Xiuzhang Zhang

Abstract

The effect of an isolated canyon interrupting a long continental shelf of constant cross section on the along-isobath, oscillatory motion of a homogeneous, incompressible fluid is considered by employing laboratory experiments (physical models) and a numerical model. The laboratory experiments are conducted in two separate cylindrical test cells of 13.0- and 1.8-m diameters, respectively. In both experiments the shelf topography is constructed around the periphery of the test cells, and the oscillatory motion is realized by modulating the rotation rate of the turntables. The numerical model employs a long shelf in a rectangular Cartesian geometry. It is found from the physical experiments that the oscillatory flow drives two characteristic flow patterns depending on the values of the temporal Rossby number, Ro t , and the Rossby number, Ro. For sufficiently small Ro t , and for the range of Ro investigated, cyclonic vortices are formed during the right to left portion of the oscillatory cycle, facing toward the deep water, on (i) the inside right and (ii) the outside left of the canyon; that is, the cyclone regime. For sufficiently large Ro t and the range of Ro studied, no closed cyclonic eddy structures are formed, a flow type designated as cyclone free.

The asymmetric nature of the right to left and left to right phases of the oscillatory, background flow leads to the generation of a mean flow along the canyon walls, which exits the canyon region on the right, facing toward the deep water, and then continues along the shelf break before decaying downstream. A parametric study of the physical and numerical model experiments is conducted by plotting the normalized maximum mean velocity observed one canyon width downstream of the canyon axis against the normalized excursion amplitude X. These data show good agreement between the physical experiments and the numerical model. For X ≥ 0.4, the normalized, maximum, mean velocity is independent of X and is roughly equal to 0.6; i.e., the maximum mean velocity is approximately equal to the mean forcing velocity over one half of the oscillatory cycle (these experiments are all of the cyclone flow type). For X ≤ 0.4, the normalized maximum mean velocity separates into (i) a lower branch for which the mean flow is relatively small and increases with X (cyclone-free flow type) and (ii) an upper branch for which the mean flow is relatively large and decreases with X (cyclone flow type).

The time-dependent nature of the large-scale eddy field for a numerical model run in the cyclone regime is shown to agree well qualitatively with physical experiments in the same regime. Time-mean velocity and streamfunction fields obtained from the numerical model are also shown to agree well with the laboratory experiments. Comparisons are also made between the present model findings and some oceanic observations and findings from other models.

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Don L. Boyer
,
Dale B. Haidvogel
, and
Nicolas Pérenne

Abstract

An integrated set of laboratory and numerical-model experiments has been conducted to understand the development of residual circulation surrounding a coastal canyon and to explore further the degree to which laboratory experiments can provide useful benchmark datasets for numerical models of the coastal ocean. The use of an idealized shear-stress boundary condition along the coastal floor in the numerical model gives good quantitative agreement with the laboratory results for the zeroth-order, time-dependent flow and good qualitative agreement for the higher-order [i.e., O(Ro), where Ro (the Rossby number) is small] time-mean flow. The quantitative agreement for the latter, however, is not within estimates of laboratory uncertainties. It is shown that the use of a no-slip condition along the floor improves the model away from the canyon boundaries, but the enhanced viscosities needed to obtain numerical stability give boundary layers that are too wide along the coastline. The laboratory and numerical-model results are used to investigate the trends of a number of flow diagnostics with changes in the governing parameters. A scaling argument to estimate the characteristic strength of the horizontal component of the time-mean or residual velocity U 1 leads to the relation U 1 /u 0 ∼ [Ro(h S / h D )−1 Ro−1 t Bu−1/2Ek−1/2], where u 0 is the amplitude of the oscillatory background flow at the shelfbreak level, (h S /h D ) is the ratio of the depth of the shelf to that of the deep ocean, Ro t is the temporal Rossby number, Bu is the Burger number, and Ek is the Ekman number. Laboratory and numerical data support this scaling. The model-to-model comparisons indicate that, for the range of parameters investigated, upwelling dominates the residual flow patterns in the vicinity of the shelf break and above. This study supports the notion that a closely coupled laboratory–numerical model investigation can lead to results that are more reliable than those obtained by either approach alone.

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Sergey I. Voropayev
,
Grady B. McEachern
,
Don L. Boyer
, and
Harindra J. S. Fernando

Abstract

The aim of this contribution is to present the results of laboratory experiments on the dynamics of basic self-propagating vortices generated in a large volume of fluid when a linear (P) and an angular (M) momentum are applied locally to a fluid. Using the method proposed, it is possible to generate a whole family of isolated (net vorticity is equal to zero) vortices with different values of the nondimensional parameter ε, which is proportional to the ratio of linear to angular momentum (ε ∝ RP/M, R is the eddy size). Typical examples include monopole (ε = 0), quasi monopole (ε = 0.1–0.3), quasi dipole (ε ≈ 1), and dipole (ε = ∞).

One of the possible applications is the dynamics of oceanic eddies. Recently, Stern and Radko considered theoretically and numerically a symmetric barotropic eddy, which is subject to a relatively small amplitude disturbance of unit azimuthal wavenumber on an f plane. This case corresponds to a self-propagating quasi monopole. They analyzed the structure of the eddy and predicted that such an eddy remains stable and could propagate a significant distance away from its origin. This effect may be of importance for oceanographic applications and such an eddy was reproduced in laboratory experiments with the purpose of verifying these theoretical predictions.

Another possible application may include large eddies behind maneuvering bodies. Recent experiments by Voropayev et al. show that, when a submerged self-propelled body accelerates, significant linear momentum is transported to the fluid and unusually large dipoles are formed in a late stratified wake. When such a body changes its direction of motion, an angular momentum is also transported to the fluid and the resulting structure will depend on the value of ε.

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Jacques Verron
,
Dominique Renouard
,
Gabriel Chabert D'Hieres
,
Thong Nguyen
,
Henri Didelle
, and
Don L. Boyer

Abstract

Alongshore oscillatory flows over an elongated topographic feature next to a vertical wall for a homogeneous, rotating fluid were investigated by means of numerical and laboratory experiments. The physical experiments were conducted in the Grenoble 13-m diameter rotating tank, in which an elongated obstacle of limited longitudinal extent was placed along the vertical sidewall. The background oscillating motion was obtained by periodically varying the platform angular velocity. Fluid motions were visualized and quantified by direct velocity measurements and particle tracking. The numerical model employed was a tridimensional model developed by Haidvogel et al. It consists of the traditional primitive equations, that is, the Navier-Stokes equations for a rotating fluid with the addition of the hydrostatic, Boussinesq, and incompressibility approximations. (The experiments described here employ the homogeneous version.) The numerical formulation uses finite differences in the horizontal and spectral representation in the vertical dimensions.

Both the laboratory and numerical experiments show that in the range of dimensionless parameters considered, two distinct flow regimes, based on general properties of the rectified flow patterns observed, can be defined. It is further shown that the flow regime designation depends principally on the magnitude of the temporal Rossby number, Ro t , defined as the ratio of the flow oscillation to the background rotation frequency. Good qualitative and quantitative agreement is found between the laboratory experiments and the numerical model for such observables as the spatial distribution of rectified flow patterns. Several other flow observables are defined and their relation with the system parameters delineated.

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Don L. Boyer
,
Joel Sommeria
,
Andjelka Srdic Mitrovic
,
V. K. Chaitanya Pakala
,
Sergey A. Smirnov
, and
Dieter Etling

Abstract

Previous laboratory experiments and associated numerical models of laminar flows forced by oscillatory, along-shelf background currents are extended to include some of the effects of boundary-generated turbulence. The experiments are conducted in the 13-m-diameter rotating-flow facility in Grenoble, France. Two pairs of case studies, one at a large forcing velocity (designated as FAST) for which the boundary layers are fully turbulent during part of the flow cycle and one at relatively smaller forcing (SLOW) for which transitional boundary layers are operative at the higher speeds of the background flow, are conducted. Smooth and artificially roughened boundaries are considered, respectively, for each of these pairs. Phase-averaged and time-mean velocity, vertical vorticity, and horizontal divergence fields are found to be qualitatively similar to those of previous laminar experiments. The similarities in the time-mean fields are that (i) within the canyon they are dominated by cyclonic vorticity with maxima centered near the shelf break; (ii) within and in the vicinity of the canyon the general circulation pattern includes a net transport into the canyon through its mouth, a net upwelling in the canyon interior, a transport away from the canyon over the shelf break along both sides of the canyon, and, by inference, a return flow to the deep ocean; and (iii) the interior time-mean flow is characterized by a well-defined coastal current whose axis follows the shelf in the vicinity of the shelf break, with the coast on the right. It is found that the measurements of the characteristic speed of the residual or time-mean flow within the canyon for the transitional and fully turbulent experiments do not follow the scaling law derived earlier for laminar experiments. An alternative scaling analysis for large-Reynolds-number flows is thus derived. Although sufficient numbers of experiments are not available to test the hypothesis fully, the measurements available for the fully turbulent flows are consistent with the theory advanced.

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Don L. Boyer
,
Gabriel Chabert d'Hieres
,
Henri Didelle
,
Jacques Verron
,
Rui-Rong Chen
, and
Lijun Tao

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)=Ω01sinωt, 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 the anticyclonic current varies with the various system parameters. The laboratory findings are in good agreement with the scaling analysis and with the theoretical model of Wright and Loder.

A nonlinear numerical model, using the quasi-geostrophic potential vorticity equation, is considered; the results correlate well with the scaling analysis and the laboratory experiments. The laboratory and numerical experiments are used to estimate the magnitude of the mean anticyclonic motion that might be expected in the vicinity of Fieberling Guyot. Future laboratory and numerical experiments will consider the additional feature of background stratification.

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