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- Author or Editor: Richard P. Mied x

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## Abstract

The seasonal thermocline in the Sargasso Sea near 30°45′N, 71°45′W was measured in July 1981 using a towed thermistor army with ∼0.5 m horizontal and vertical resolution. A 200-km long section of the survey path is analyzed for overturn occurrences and the relationship of these occurrences to the ambient flow field. Our analysis shows that the probability of an overturn occurrences increases when the Richardson number of the ambient field decreases. This increase is most rapid when the Richardson number is of order unity. Our assessment of overturn processes based on calculated conditional probabilities indicates that both sheer instability and advective instability are important to the generation of the overtures observed in our experiment while the symmetric instability is not.

## Abstract

The seasonal thermocline in the Sargasso Sea near 30°45′N, 71°45′W was measured in July 1981 using a towed thermistor army with ∼0.5 m horizontal and vertical resolution. A 200-km long section of the survey path is analyzed for overturn occurrences and the relationship of these occurrences to the ambient flow field. Our analysis shows that the probability of an overturn occurrences increases when the Richardson number of the ambient field decreases. This increase is most rapid when the Richardson number is of order unity. Our assessment of overturn processes based on calculated conditional probabilities indicates that both sheer instability and advective instability are important to the generation of the overtures observed in our experiment while the symmetric instability is not.

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## Abstract

This paper addresses the tendency for an eastward-propagating modon to form from a mesoscale eddy which has an inclined vertical axis and different senses of rotation in the upper and deep oceans. This scenario, which has been observed in nature (McCartney *et al*., 1978; Savehenko *et al*., 1978), is modeled in a two-layer ocean by placing a cyclonic eddy in the upper ocean, and an anticyclonic eddy in the deep ocean; these two eddies have centers which are horizontally separated. Inferences about the tendency for modongenesis are made from analytical quasigeostrophic calculations and numerical primitive equation computations. Numerical experiments have been performed using radial velocity distributions ∝ *r* exp(−*r*
^{2}/2*L*
^{2}) in each layer. These results not only corroborate the analytical early-time inferences but expand the parameter range for which modongenesis occurs.

If the upper wean vortex is cyclonic and lies due north of the deep ocean anticyclonic gyre, modongenesis occurs when the vortex centers are separated by ≲(1.5−2.0)*L*. But if the deep wean anticyclonic vortex is due north of the cyclonic one, modongenesis ensues when the separation is ≲*L*/3. The maximum separation at which modongenesis can occur varies continuously between these two extremes as the line of vortex centers is rotated from one configuration to the other. The modons so formed possess a barotropic core (Latichey and Reznik, 1976), and support superposed barotropic and baroclinic vortices (Stern, 1975; Flierl *et al*., 1980), the propagation speeds, length scales and strengths of the resulting modons are examined in the light of these steady state theories.

## Abstract

This paper addresses the tendency for an eastward-propagating modon to form from a mesoscale eddy which has an inclined vertical axis and different senses of rotation in the upper and deep oceans. This scenario, which has been observed in nature (McCartney *et al*., 1978; Savehenko *et al*., 1978), is modeled in a two-layer ocean by placing a cyclonic eddy in the upper ocean, and an anticyclonic eddy in the deep ocean; these two eddies have centers which are horizontally separated. Inferences about the tendency for modongenesis are made from analytical quasigeostrophic calculations and numerical primitive equation computations. Numerical experiments have been performed using radial velocity distributions ∝ *r* exp(−*r*
^{2}/2*L*
^{2}) in each layer. These results not only corroborate the analytical early-time inferences but expand the parameter range for which modongenesis occurs.

If the upper wean vortex is cyclonic and lies due north of the deep ocean anticyclonic gyre, modongenesis occurs when the vortex centers are separated by ≲(1.5−2.0)*L*. But if the deep wean anticyclonic vortex is due north of the cyclonic one, modongenesis ensues when the separation is ≲*L*/3. The maximum separation at which modongenesis can occur varies continuously between these two extremes as the line of vortex centers is rotated from one configuration to the other. The modons so formed possess a barotropic core (Latichey and Reznik, 1976), and support superposed barotropic and baroclinic vortices (Stern, 1975; Flierl *et al*., 1980), the propagation speeds, length scales and strengths of the resulting modons are examined in the light of these steady state theories.

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## Abstract

Numerical simulations of the propagation of cyclonic Gulf Stream rings are made using a primitive equation β-plane model of a flat-bottomed two-layer ocean with a rigid lid. Initially circular eddies having, upper and deep ocean maximum currents max*U*
_{1} and max*U*
_{2} located at radial position *l* from the center are allowed to evolve and four types of behavior have been discerned: 1) dispersing rings possess negligible nonlinearity and disperse rapidly; 2) barotropic rings (*U*
_{1} = *U*
_{2}) are weakly dispersive, propagating recognizably for long periods of time, and, nearly barotropic eddies (*U*
_{1} ≈ *U*
_{2}) slowly lose coherence in the deep ocean; 3) upper ocean rings propagate with a vortex present only in the upper ocean; and 4) eastward-traveling eddies possess circulations in the upper and lower oceans which propagate together stably to the cast.

Changes in viscosity are found to be more important to the longevity of the ring than are changes in (max*U*
_{1})/β*l*
^{2}. Both westward and northward speeds increase with increasing max*U*
_{2}/max*U*
_{1} and increasing (max*U*
_{1})/β*l*
^{2}. Speeds to the west are found to be 2–3 km day^{−1} and those to the north are 1–9 km day^{−1} for 3 ≲ (max*U*
_{1})/β*l*
^{2} ≲ 15 and 0 ⩽ max*U*
_{2})/max*U*
_{1} ⩽ 1.2.

## Abstract

Numerical simulations of the propagation of cyclonic Gulf Stream rings are made using a primitive equation β-plane model of a flat-bottomed two-layer ocean with a rigid lid. Initially circular eddies having, upper and deep ocean maximum currents max*U*
_{1} and max*U*
_{2} located at radial position *l* from the center are allowed to evolve and four types of behavior have been discerned: 1) dispersing rings possess negligible nonlinearity and disperse rapidly; 2) barotropic rings (*U*
_{1} = *U*
_{2}) are weakly dispersive, propagating recognizably for long periods of time, and, nearly barotropic eddies (*U*
_{1} ≈ *U*
_{2}) slowly lose coherence in the deep ocean; 3) upper ocean rings propagate with a vortex present only in the upper ocean; and 4) eastward-traveling eddies possess circulations in the upper and lower oceans which propagate together stably to the cast.

Changes in viscosity are found to be more important to the longevity of the ring than are changes in (max*U*
_{1})/β*l*
^{2}. Both westward and northward speeds increase with increasing max*U*
_{2}/max*U*
_{1} and increasing (max*U*
_{1})/β*l*
^{2}. Speeds to the west are found to be 2–3 km day^{−1} and those to the north are 1–9 km day^{−1} for 3 ≲ (max*U*
_{1})/β*l*
^{2} ≲ 15 and 0 ⩽ max*U*
_{2})/max*U*
_{1} ⩽ 1.2.

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## Abstract

The authors address the propagation of continental shelf waves in the Mid-Atlantic Bight. An analytical model of the bathymetry in the region is constructed by representing the continental shelf as a gently sloping bottom, which deepens linearly with offshore distance to the place where it meets the continental slope. Seaward of that point, the bathymetry is modeled with an exponentially decaying function of distance. The linearized, barotropic equations of hydrostatic motion, subject to the long-wave approximation, yield separate shelf and slope solutions, which are matched at the shelf break to specify the eigenfunctions. The associated eigenvalues define the dispersion relations for each of the modes. Wavenumber–frequency pairs derived from NOAA sea surface height stations along the coast are plotted on the first-mode dispersion curve, and the agreement is good. The theory also shows good agreement with the wave data of D. P. Wang.

## Abstract

The authors address the propagation of continental shelf waves in the Mid-Atlantic Bight. An analytical model of the bathymetry in the region is constructed by representing the continental shelf as a gently sloping bottom, which deepens linearly with offshore distance to the place where it meets the continental slope. Seaward of that point, the bathymetry is modeled with an exponentially decaying function of distance. The linearized, barotropic equations of hydrostatic motion, subject to the long-wave approximation, yield separate shelf and slope solutions, which are matched at the shelf break to specify the eigenfunctions. The associated eigenvalues define the dispersion relations for each of the modes. Wavenumber–frequency pairs derived from NOAA sea surface height stations along the coast are plotted on the first-mode dispersion curve, and the agreement is good. The theory also shows good agreement with the wave data of D. P. Wang.

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## Abstract

In this paper steadily rotating modons that are trapped over topographic features with finite horizontal length scales are described. The quasigeostrophic equation over topography is transformed to a frame rotating with angular frequency ω, and steady solutions are sought that decay monotonically outside of a circle of radius, *r*=*r*
_{
a
}. These conditions are imposed upon an isolated seamount or depression of the form η=*h*
_{0}[1−(*r*/*r*
_{
b
})^{
m
}] (and η=0 for *r*≥*r*
_{
b
}) with primary focus on the *m*=2 case. Two different scenarios result from this choice of topography and correspond to *r*
_{
a
}/*r*
_{
b
}=α^{½}≥1 or α^{½}≤1. There are three solution regions compared with the usual two for rectilinear modons. Both scenarios result in a countable infinity of both radial and azimuthal modes. In addition, it is found that an axisymmetric flow with a particular form but arbitrary amplitude can be added to the basic modon multipole solutions. The angular frequency is then found as a function of α and this axisymmetric flow amplitude. Topographically trapped rotating modons can spin clockwise or anticlockwise.

## Abstract

In this paper steadily rotating modons that are trapped over topographic features with finite horizontal length scales are described. The quasigeostrophic equation over topography is transformed to a frame rotating with angular frequency ω, and steady solutions are sought that decay monotonically outside of a circle of radius, *r*=*r*
_{
a
}. These conditions are imposed upon an isolated seamount or depression of the form η=*h*
_{0}[1−(*r*/*r*
_{
b
})^{
m
}] (and η=0 for *r*≥*r*
_{
b
}) with primary focus on the *m*=2 case. Two different scenarios result from this choice of topography and correspond to *r*
_{
a
}/*r*
_{
b
}=α^{½}≥1 or α^{½}≤1. There are three solution regions compared with the usual two for rectilinear modons. Both scenarios result in a countable infinity of both radial and azimuthal modes. In addition, it is found that an axisymmetric flow with a particular form but arbitrary amplitude can be added to the basic modon multipole solutions. The angular frequency is then found as a function of α and this axisymmetric flow amplitude. Topographically trapped rotating modons can spin clockwise or anticlockwise.

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## Abstract

Numerical simulations have been performed to understand the generation and evolution of mushroom-like patterns observed in remote sensing images of the ocean surface. A two-layer, shallow-water model is employed using a periodic channel on an *f*-plane. The model is initialized with a unidirectional upper-Ocean momentum patch; the lower layer is at rest, and there is no initial interface displacement. A tracer is used to simulate the presence of passive ocean surface fields advected by the flow. The model thus simulates a nonlinear geostrophic adjustment process at finite Rossby number with a strong radiated wave field and rapid tracer advection. Several types of tracer configuration result, depending upon the size of the Rossby number and the ratio of the patch size to the internal deformation radius. The values of these parameters determine the degree of symmetry of the mushroom pattern, or whether a mushroom tracer distribution even results from the initial flow field. The numerical model is always operated with the ratio of upper layer to lower layer heights small, and analytical calculations using the reduced-gravity, shallow-water equations are used to interpret the numerical results.

## Abstract

Numerical simulations have been performed to understand the generation and evolution of mushroom-like patterns observed in remote sensing images of the ocean surface. A two-layer, shallow-water model is employed using a periodic channel on an *f*-plane. The model is initialized with a unidirectional upper-Ocean momentum patch; the lower layer is at rest, and there is no initial interface displacement. A tracer is used to simulate the presence of passive ocean surface fields advected by the flow. The model thus simulates a nonlinear geostrophic adjustment process at finite Rossby number with a strong radiated wave field and rapid tracer advection. Several types of tracer configuration result, depending upon the size of the Rossby number and the ratio of the patch size to the internal deformation radius. The values of these parameters determine the degree of symmetry of the mushroom pattern, or whether a mushroom tracer distribution even results from the initial flow field. The numerical model is always operated with the ratio of upper layer to lower layer heights small, and analytical calculations using the reduced-gravity, shallow-water equations are used to interpret the numerical results.

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## Abstract

Acoustic Doppler profiler measurements of inertial waves embedded within the high shell region of a cold core ring in the Sargasso Sea are described. By repeatedly traversing the same point from different directions, a sampling pattern resembling an asterisk was obtained. The data reveal the presence of two different wave signals which are advected through the test region: a strong, monochromatic, downgoing wave, and a less well defined ensemble of mostly downgoing waves. Calculations of the phase of the vertical shear and coherence in the vertical and horizontal planes establishes the horizontal and vertical wavenumbers. These are 33 m and 11.8 km, respectively, and the wave propagates in a nearly cross-stream direction. The weaker ensemble of waves advected through the test region later in the experiment has similar dominant scales: ∼30 m in the vertical and a horizontal wavelength in the range 11.6–30.0 km. For all of these waves, the ratio of vertical to horizontal wavelength is small and the intrinsic frequency is 1.09*f*, so that the waves are of near-inertial frequency. By examining individual terms in the near-inertial ray equations, it is seen that the horizontal crosscurrent variations cause the horizontal wavenumber to be rotated so as to propagate perpendicular to the current. Consideration of the full ray equations for all internal wave frequencies in a barotropic current shows a filtering effect that also preserves waves propagating across the current. Both of these results are consistent with the observation that the waves are propagating nearly cross stream.

## Abstract

Acoustic Doppler profiler measurements of inertial waves embedded within the high shell region of a cold core ring in the Sargasso Sea are described. By repeatedly traversing the same point from different directions, a sampling pattern resembling an asterisk was obtained. The data reveal the presence of two different wave signals which are advected through the test region: a strong, monochromatic, downgoing wave, and a less well defined ensemble of mostly downgoing waves. Calculations of the phase of the vertical shear and coherence in the vertical and horizontal planes establishes the horizontal and vertical wavenumbers. These are 33 m and 11.8 km, respectively, and the wave propagates in a nearly cross-stream direction. The weaker ensemble of waves advected through the test region later in the experiment has similar dominant scales: ∼30 m in the vertical and a horizontal wavelength in the range 11.6–30.0 km. For all of these waves, the ratio of vertical to horizontal wavelength is small and the intrinsic frequency is 1.09*f*, so that the waves are of near-inertial frequency. By examining individual terms in the near-inertial ray equations, it is seen that the horizontal crosscurrent variations cause the horizontal wavenumber to be rotated so as to propagate perpendicular to the current. Consideration of the full ray equations for all internal wave frequencies in a barotropic current shows a filtering effect that also preserves waves propagating across the current. Both of these results are consistent with the observation that the waves are propagating nearly cross stream.

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## Abstract

This paper deals with flow in a rectilinear channel on a rotating earth. The flow is directed perpendicular to the background planetary vorticity; both an analytical theory and numerical simulations are employed. The analytical approach assumes the existence of an eddy viscosity and employs a perturbation expansion in powers of the reciprocal of the Rossby number (Ro). At lowest order, a cross-channel circulation arises because of the tilting of the planetary vorticity vector by the shear in the along-channel direction. This circulation causes a surface convergence, which achieves its maximum value at a channel aspect ratio (= width/depth) of approximately 10. The location of the maximum surface convergence moves from near the center of the channel to a position very near the sidewalls as the aspect ratio increases from *O*(1) to *O*(100). To include the effects of turbulence, direct numerical pseudospectral simulations of the equations of motion are employed. While holding the friction Reynolds number fixed at 230.27, a series of simulations with increasing rotation (Ro = ∞, 10, 1.0, 0.1) are performed. The channelwide circulation cell observed in the analytical theory occurs for the finite Rossby number, but is displaced by lateral self-advection. In addition, turbulence-driven corner circulations appear, which make the along-channel maximum velocity appear at a subsurface location. The most interesting effect is the segregation of the turbulence to one side of the channel, while the turbulence is suppressed on the opposite side.

## Abstract

This paper deals with flow in a rectilinear channel on a rotating earth. The flow is directed perpendicular to the background planetary vorticity; both an analytical theory and numerical simulations are employed. The analytical approach assumes the existence of an eddy viscosity and employs a perturbation expansion in powers of the reciprocal of the Rossby number (Ro). At lowest order, a cross-channel circulation arises because of the tilting of the planetary vorticity vector by the shear in the along-channel direction. This circulation causes a surface convergence, which achieves its maximum value at a channel aspect ratio (= width/depth) of approximately 10. The location of the maximum surface convergence moves from near the center of the channel to a position very near the sidewalls as the aspect ratio increases from *O*(1) to *O*(100). To include the effects of turbulence, direct numerical pseudospectral simulations of the equations of motion are employed. While holding the friction Reynolds number fixed at 230.27, a series of simulations with increasing rotation (Ro = ∞, 10, 1.0, 0.1) are performed. The channelwide circulation cell observed in the analytical theory occurs for the finite Rossby number, but is displaced by lateral self-advection. In addition, turbulence-driven corner circulations appear, which make the along-channel maximum velocity appear at a subsurface location. The most interesting effect is the segregation of the turbulence to one side of the channel, while the turbulence is suppressed on the opposite side.

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## Abstract

This work examines the presence of internal-inertial waves in a front in the North Atlantic subtropical convergence zone. Results of Doppler shear profiler and towed thermistor chain surveys are displayed to document the position and magnitude of the front. Objective maps of the total measured velocity are computed and subtracted from the observed velocity fields. The remaining wave signal is processed to yield horizontal (towed) and vertical (dropped) kinetic energy spectra across the front. From these, rotary spectra are also computed along the line of tow and in the vertical to determine the horizontal and vertical anisotropy. It is found that several nearly monochromatic waves are propagating northward and southward from the front with horizontal length scales of ∼32–50 km. It was also discovered that the region of anticyclonic frontal vorticity exhibits an excess of downgoing energy at the longest vertical wavelength thus sampled (∼50 m), while the region of cyclonic vorticity possesses more upgoing than downgoing energy at the same wavelengths. Vertical and horizontal spectra variances of the total kinetic energy within the region of the front am each enhanced by a factor of about five over the variances outside the front. These results are discussed in the light of recent work by Kunze.

## Abstract

This work examines the presence of internal-inertial waves in a front in the North Atlantic subtropical convergence zone. Results of Doppler shear profiler and towed thermistor chain surveys are displayed to document the position and magnitude of the front. Objective maps of the total measured velocity are computed and subtracted from the observed velocity fields. The remaining wave signal is processed to yield horizontal (towed) and vertical (dropped) kinetic energy spectra across the front. From these, rotary spectra are also computed along the line of tow and in the vertical to determine the horizontal and vertical anisotropy. It is found that several nearly monochromatic waves are propagating northward and southward from the front with horizontal length scales of ∼32–50 km. It was also discovered that the region of anticyclonic frontal vorticity exhibits an excess of downgoing energy at the longest vertical wavelength thus sampled (∼50 m), while the region of cyclonic vorticity possesses more upgoing than downgoing energy at the same wavelengths. Vertical and horizontal spectra variances of the total kinetic energy within the region of the front am each enhanced by a factor of about five over the variances outside the front. These results are discussed in the light of recent work by Kunze.