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## Abstract

A linear, small amplitude model of Rossby waves forced by idealized meanders is presented in order to ascertain whether or not the observed low frequency motions near the Gulf Stream are capable of being so generated. Two crucial ingredients are shown to be necessary; the meandering activity must vary in the downstream direction and the meanders must have a transient behavior. Cast as a stochastic average over a large number of meanders the predicted amplitudes of the kinetic energy and Reynolds stresses are similar to those observed. Implications for the forcing of a mean flow are discussed.

## Abstract

A linear, small amplitude model of Rossby waves forced by idealized meanders is presented in order to ascertain whether or not the observed low frequency motions near the Gulf Stream are capable of being so generated. Two crucial ingredients are shown to be necessary; the meandering activity must vary in the downstream direction and the meanders must have a transient behavior. Cast as a stochastic average over a large number of meanders the predicted amplitudes of the kinetic energy and Reynolds stresses are similar to those observed. Implications for the forcing of a mean flow are discussed.

## Abstract

Several schemes for correcting temperature and velocity measurements from moored current meters are tested on two moorings, one of which experienced large vertical excursions as the Gulf Stream meandered over it. The addition of two extra temperature recorders 100 m above and below the current meter permits the calculation of a reference corrected series through time dependent interpolation. By assuming that the current meter profiles the vertical temperature structure as it is pulled up and down it is possible to calculate the mean vertical temperature gradient and its dependence on temperature. A quadratic dependence is suggested by hydrographic measurements and the direct in situ measurements on the moorings. It is found possible, through weighted polynomial regression, to calculate this dependence directly from measurements of temperature and pressure on a single instrument and, thereby, to remove more than 95 percent of the mooring motion induced temperature variance. The correction of temperature for mooring motion is found necessary for accurate estimation of heat flux from moorings in energetic areas.

Correction of velocity is more difficult but it is not found to have much effect on flux calculations.

## Abstract

Several schemes for correcting temperature and velocity measurements from moored current meters are tested on two moorings, one of which experienced large vertical excursions as the Gulf Stream meandered over it. The addition of two extra temperature recorders 100 m above and below the current meter permits the calculation of a reference corrected series through time dependent interpolation. By assuming that the current meter profiles the vertical temperature structure as it is pulled up and down it is possible to calculate the mean vertical temperature gradient and its dependence on temperature. A quadratic dependence is suggested by hydrographic measurements and the direct in situ measurements on the moorings. It is found possible, through weighted polynomial regression, to calculate this dependence directly from measurements of temperature and pressure on a single instrument and, thereby, to remove more than 95 percent of the mooring motion induced temperature variance. The correction of temperature for mooring motion is found necessary for accurate estimation of heat flux from moorings in energetic areas.

Correction of velocity is more difficult but it is not found to have much effect on flux calculations.

## Abstract

The flow of a single layer of fluid along a channel of variable dimensions is hydraulically controlled when long gravity waves can no longer propagate upstream at the cross-section of minimum area. For a multilayer fluid, it is shown that a controlled situation exists when there is a separate geometrical extremum for each of the gravity wave modes. The structure of each control section must be different, reflecting the different vertical structures of the internal modes.

A channel with three layers of different density is studied in some detail as an analogue to the principal water masses in the Alboran Sea and Strait of Gibraltar. With the lowest layer at rest and the surface rigid, the control for the slowest second internal mode is primarily a width contraction while that for the first mode must also involve a reduction in bottom depth. The problem separates into control problems for each mode. That for the first mode is a classic lock exchange problem with just two layers (controlled at the Strait of Gibraltar) while that for the second mode reduces to that for a single layer (suggested to be controlled at Alboran Strait).

For the Alboran Sea rotational effects are important, particularly at the second-mode control point. With these included the principal qualitative features of the circulation are reproduced. Anticyclonic vorticity is produced in both the Atlantic Water and the Levantine Intermediate Water as both are vertically compressed upon entering the Western Alboran Sea through the two control points. The Deep Mediterranean Water is uplifted at the second-mode control point (Alboran Strait) and is banked against the southern wall thereafter as the intermediate water separates from the wall. A secondary circulation is forced in the upper layer which causes southward, cross-channel flow to the west of Alboran Island.

## Abstract

The flow of a single layer of fluid along a channel of variable dimensions is hydraulically controlled when long gravity waves can no longer propagate upstream at the cross-section of minimum area. For a multilayer fluid, it is shown that a controlled situation exists when there is a separate geometrical extremum for each of the gravity wave modes. The structure of each control section must be different, reflecting the different vertical structures of the internal modes.

A channel with three layers of different density is studied in some detail as an analogue to the principal water masses in the Alboran Sea and Strait of Gibraltar. With the lowest layer at rest and the surface rigid, the control for the slowest second internal mode is primarily a width contraction while that for the first mode must also involve a reduction in bottom depth. The problem separates into control problems for each mode. That for the first mode is a classic lock exchange problem with just two layers (controlled at the Strait of Gibraltar) while that for the second mode reduces to that for a single layer (suggested to be controlled at Alboran Strait).

For the Alboran Sea rotational effects are important, particularly at the second-mode control point. With these included the principal qualitative features of the circulation are reproduced. Anticyclonic vorticity is produced in both the Atlantic Water and the Levantine Intermediate Water as both are vertically compressed upon entering the Western Alboran Sea through the two control points. The Deep Mediterranean Water is uplifted at the second-mode control point (Alboran Strait) and is banked against the southern wall thereafter as the intermediate water separates from the wall. A secondary circulation is forced in the upper layer which causes southward, cross-channel flow to the west of Alboran Island.

## Abstract

Observations of the vertical and horizontal structure of motions near Bermuda have been made with two long-term moored arrays, one relatively far from and the other close to the island. Although not coincident in time, both arrays see horizontally coherent motions at 11 frequency bands ranging in period from 405 to 9.8 h. Only a peak at 26.1 h appears to be significant in the autospectra and, on several grounds, this is identified with the fundamental island-trapped mode (vertically and azimuthally).

Additional resonant subinertial periods are at roughly 45, 54 and 90 h and these are vertical modes 2, 3 or 4 and azimuthal modes 1 or 2 propagating clockwise. The superinertial modes have less internal consistency but appear to have higher order vertical and azimuthal structures and both senses of azimuthal phase propagation.

The subinertial vertical structure is modal and can be rationalized with baroclinic wave dynamics on a sloping bottom by defining an effective bottom depth as some reasonable average over the offshore decay scale.

The subinertial motions are coherent with the surface wind stress and the phase between this forcing and the response changes by 180° across the trapped wave frequency bands consistent with a resonant system. The *Q* of the 26.1 h peak is at least 20 implying that dissipation has only a slight influence on the dynamics.

## Abstract

Observations of the vertical and horizontal structure of motions near Bermuda have been made with two long-term moored arrays, one relatively far from and the other close to the island. Although not coincident in time, both arrays see horizontally coherent motions at 11 frequency bands ranging in period from 405 to 9.8 h. Only a peak at 26.1 h appears to be significant in the autospectra and, on several grounds, this is identified with the fundamental island-trapped mode (vertically and azimuthally).

Additional resonant subinertial periods are at roughly 45, 54 and 90 h and these are vertical modes 2, 3 or 4 and azimuthal modes 1 or 2 propagating clockwise. The superinertial modes have less internal consistency but appear to have higher order vertical and azimuthal structures and both senses of azimuthal phase propagation.

The subinertial vertical structure is modal and can be rationalized with baroclinic wave dynamics on a sloping bottom by defining an effective bottom depth as some reasonable average over the offshore decay scale.

The subinertial motions are coherent with the surface wind stress and the phase between this forcing and the response changes by 180° across the trapped wave frequency bands consistent with a resonant system. The *Q* of the 26.1 h peak is at least 20 implying that dissipation has only a slight influence on the dynamics.

## Abstract

Observations from a recent field experiment in the Vema Channel are briefly described. These show a remarkable change in the configuration of isopycnal surfaces within the channel and the development of thick, nearly homogeneous regions near the bottom which are capped by sharp vertical gradients. Contrary to previous speculation that these “bottom boundary layer” result from enhanced vertical mixing, a dynamical mechanism is explored. This involves the hydraulic adjustment of an inertial, semi-geostrophic flow to the channel geometry.

First, an active two-layer flow in a rectangular geometry is studied to show that internal flow separation can occur when the flow is accelerated sufficiently by a narrowing channel. Almost always this separation accompanies hydraulic control: the slowest upstream moving Kelvin wave is stopped and upstream and downstream states are not symmetric with respect to the channel width. An active three-layer flow with a variable bottom profile is then presented as a more accurate model of the Vema Channel. The crucial geometrical ingredient appears to be the growth of a plateau on the eastern side of the channel: this confines the deepest layer laterally but it has more of a sill effect upon the upper layers. Many of the observed features of the flow are explained by this model including the changing layer shapes, flow separation, and the reverse flow found above the plateau.

A major disagreement is that the flow in the furthest downstream section does not appear to be separated, but more closely resembles that at the entrance. It is suggested that upstream of this last section a hydraulic jump occurs returning the flow to a subcritical state of lower energy. Consistent with this idea the potential energy of the deeper layers increases, and the wave perturbation amplitudes have the correct tendency.

## Abstract

Observations from a recent field experiment in the Vema Channel are briefly described. These show a remarkable change in the configuration of isopycnal surfaces within the channel and the development of thick, nearly homogeneous regions near the bottom which are capped by sharp vertical gradients. Contrary to previous speculation that these “bottom boundary layer” result from enhanced vertical mixing, a dynamical mechanism is explored. This involves the hydraulic adjustment of an inertial, semi-geostrophic flow to the channel geometry.

First, an active two-layer flow in a rectangular geometry is studied to show that internal flow separation can occur when the flow is accelerated sufficiently by a narrowing channel. Almost always this separation accompanies hydraulic control: the slowest upstream moving Kelvin wave is stopped and upstream and downstream states are not symmetric with respect to the channel width. An active three-layer flow with a variable bottom profile is then presented as a more accurate model of the Vema Channel. The crucial geometrical ingredient appears to be the growth of a plateau on the eastern side of the channel: this confines the deepest layer laterally but it has more of a sill effect upon the upper layers. Many of the observed features of the flow are explained by this model including the changing layer shapes, flow separation, and the reverse flow found above the plateau.

A major disagreement is that the flow in the furthest downstream section does not appear to be separated, but more closely resembles that at the entrance. It is suggested that upstream of this last section a hydraulic jump occurs returning the flow to a subcritical state of lower energy. Consistent with this idea the potential energy of the deeper layers increases, and the wave perturbation amplitudes have the correct tendency.

## Abstract

Steady flow over large-scale bathymetric changes of a uniform zonal current in a two-layer fluid is studied under the assumptions that it is geostrophic, that relative vorticity can be ignored, that variations in the planetary vorticity are important and that the upper layer is infinitely thick. This is an extension of the analytic work by Rhines to situations in which the interface can have finite deformations. As concluded by Rhines, both from a small amplitude theory and from numerical integration of the time-dependent initial value problem, there are several features of the resulting solutions that bear close resemblance to the classical channel hydraulics phenomenon. These include the downward (upward) dip of the interface when the flow is subcritical (supercritical) with respect to the long Rossby wave phase speed and the formation of sharp frontal regions downstream of the topography. With respect to the latter it is shown in this steady state analysis that the front arises, not from a hydraulic effect in the conventional sense, but from the intersection of characteristics carrying conflicting information from different parts of the boundary. Concomitant with caustic formation is an induced change in upstream conditions. The Froude number dependence is determined. For the small Froude numbers expected of the midocean deep circulation only very large topographic features such as the mid-Atlantic Ridge can be expected to induce a caustic.

## Abstract

Steady flow over large-scale bathymetric changes of a uniform zonal current in a two-layer fluid is studied under the assumptions that it is geostrophic, that relative vorticity can be ignored, that variations in the planetary vorticity are important and that the upper layer is infinitely thick. This is an extension of the analytic work by Rhines to situations in which the interface can have finite deformations. As concluded by Rhines, both from a small amplitude theory and from numerical integration of the time-dependent initial value problem, there are several features of the resulting solutions that bear close resemblance to the classical channel hydraulics phenomenon. These include the downward (upward) dip of the interface when the flow is subcritical (supercritical) with respect to the long Rossby wave phase speed and the formation of sharp frontal regions downstream of the topography. With respect to the latter it is shown in this steady state analysis that the front arises, not from a hydraulic effect in the conventional sense, but from the intersection of characteristics carrying conflicting information from different parts of the boundary. Concomitant with caustic formation is an induced change in upstream conditions. The Froude number dependence is determined. For the small Froude numbers expected of the midocean deep circulation only very large topographic features such as the mid-Atlantic Ridge can be expected to induce a caustic.

## Abstract

Using moored array data collected across the Gulf Stream at 55°W, the author has investigated the dynamic signatures of the velocity fluctuations at the thermocline (550 m) and near-bottom (4000 m) levels. The cross-stream amplitude and phase structures for motions with period from 64 to 12 days, in a coordinate frame aligned with the instantaneous stream, have a striking resemblance to those computed from small amplitude instability theory. It is the sinuous or asymmetric mode that appears to dominate the observed fluctuations as is predicted. In addition, the mean downstream velocity at the two levels is consistent with a two-layer model for the mean flow in which the lower layer has uniform potential vorticity. When fit to the data this model predicts a value for the rate of change of the Coriolis parameter appropriate to this latitude, but one would expect it to be augmented by a factor of 2 or so by the significant slope of the bottom in this region.

## Abstract

Using moored array data collected across the Gulf Stream at 55°W, the author has investigated the dynamic signatures of the velocity fluctuations at the thermocline (550 m) and near-bottom (4000 m) levels. The cross-stream amplitude and phase structures for motions with period from 64 to 12 days, in a coordinate frame aligned with the instantaneous stream, have a striking resemblance to those computed from small amplitude instability theory. It is the sinuous or asymmetric mode that appears to dominate the observed fluctuations as is predicted. In addition, the mean downstream velocity at the two levels is consistent with a two-layer model for the mean flow in which the lower layer has uniform potential vorticity. When fit to the data this model predicts a value for the rate of change of the Coriolis parameter appropriate to this latitude, but one would expect it to be augmented by a factor of 2 or so by the significant slope of the bottom in this region.

## Abstract

Several schemes are offered for the correction of temperature and velocity in the thermocline for mooring motion. They require measurements from at least two instruments spanning the thermocline and assume that the temporal variation of temperature (a proxy for density) results primarily from the vertical displacement of a fixed profile whose only degree of freedom is its pressure offset. Using two instruments in the thermocline from a mooring (the “GUSTO” mooring) in the Gulf Stream, the procedure is tested against a third on the same mooring.

## Abstract

Several schemes are offered for the correction of temperature and velocity in the thermocline for mooring motion. They require measurements from at least two instruments spanning the thermocline and assume that the temporal variation of temperature (a proxy for density) results primarily from the vertical displacement of a fixed profile whose only degree of freedom is its pressure offset. Using two instruments in the thermocline from a mooring (the “GUSTO” mooring) in the Gulf Stream, the procedure is tested against a third on the same mooring.

## Abstract

The structure of the potential vorticity flux and a mean flow induced by a topographic wave incident over a bottom slope are investigated analytically and numerically, with focus on the case that bottom friction is the dominant dissipation process. In this case it is shown that the topographic wave cannot be a steady source of the potential vorticity outside the bottom Ekman layer. Instead, the distribution of potential vorticity is determined from the initial transient of the topographic wave. This potential vorticity and the heat flux by the topographic wave at the bottom determine the mean flow and give a relation between the horizontal and vertical scales of the mean flow. When the horizontal scale of the mean flow is larger than the internal deformation radius and the potential vorticity is not so large, the mean flow is almost constant with depth independent of whether the topographic wave is bottom intensified. Then the mean flow is proportional to the divergence of the vertically integrated Reynolds stress. This divergence, which is caused by bottom friction, is large when the group velocity *c*
_{
g
} and the vertical scale *μ*
^{−1} of the wave motion are small. Thus, the mean flow tends to be large where *c*
_{
g
} and *μ*
^{−1} become small and decreases as the topographic wave is dissipated by bottom friction. Because bottom friction also dissipates the mean flow, the mean flow asymptotically approaches a constant value as the friction becomes zero. These features of the potential vorticity flux and the mean flow are reproduced in numerical experiments in which it is also shown that the distribution of the mean flow depends on the amplitude of the wave because of the Doppler shift of the wave by the mean flow. These features of the mean flow are preserved when stratification and bottom topography resembling those over the continental slope near the Gulf Stream are used. The transport of the mean flow is about 20 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) when the wave amplitude is about 2 cm s^{−1}. This transport is similar to that of the recirculation gyre in the Gulf Stream region.

## Abstract

The structure of the potential vorticity flux and a mean flow induced by a topographic wave incident over a bottom slope are investigated analytically and numerically, with focus on the case that bottom friction is the dominant dissipation process. In this case it is shown that the topographic wave cannot be a steady source of the potential vorticity outside the bottom Ekman layer. Instead, the distribution of potential vorticity is determined from the initial transient of the topographic wave. This potential vorticity and the heat flux by the topographic wave at the bottom determine the mean flow and give a relation between the horizontal and vertical scales of the mean flow. When the horizontal scale of the mean flow is larger than the internal deformation radius and the potential vorticity is not so large, the mean flow is almost constant with depth independent of whether the topographic wave is bottom intensified. Then the mean flow is proportional to the divergence of the vertically integrated Reynolds stress. This divergence, which is caused by bottom friction, is large when the group velocity *c*
_{
g
} and the vertical scale *μ*
^{−1} of the wave motion are small. Thus, the mean flow tends to be large where *c*
_{
g
} and *μ*
^{−1} become small and decreases as the topographic wave is dissipated by bottom friction. Because bottom friction also dissipates the mean flow, the mean flow asymptotically approaches a constant value as the friction becomes zero. These features of the potential vorticity flux and the mean flow are reproduced in numerical experiments in which it is also shown that the distribution of the mean flow depends on the amplitude of the wave because of the Doppler shift of the wave by the mean flow. These features of the mean flow are preserved when stratification and bottom topography resembling those over the continental slope near the Gulf Stream are used. The transport of the mean flow is about 20 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) when the wave amplitude is about 2 cm s^{−1}. This transport is similar to that of the recirculation gyre in the Gulf Stream region.

## Abstract

Previous numerical experiments with an unstable zonal jet on a *β* plane are extended to the reduced-gravity case. The strength of the resulting recirculation varies inversely with the combination *β* + 1/*S* where *S* is the Burger number and *β* the latitudinal variation of the Coriolis parameter. In addition, the centers of the antisymmetrically located gyres are located a distance from the jet inlet that varies inversely with the linear growth rate of small perturbations. An improved analytic model has also been constructed that predicts the recirculation strength and has the single unsupported assumption that the meridionally integrated potential vorticity anomaly be independent of zonal position.

## Abstract

Previous numerical experiments with an unstable zonal jet on a *β* plane are extended to the reduced-gravity case. The strength of the resulting recirculation varies inversely with the combination *β* + 1/*S* where *S* is the Burger number and *β* the latitudinal variation of the Coriolis parameter. In addition, the centers of the antisymmetrically located gyres are located a distance from the jet inlet that varies inversely with the linear growth rate of small perturbations. An improved analytic model has also been constructed that predicts the recirculation strength and has the single unsupported assumption that the meridionally integrated potential vorticity anomaly be independent of zonal position.