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- Author or Editor: Xiuzhang Zhang x

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## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.