Richard P. Mied

The occurrence of parametric instabilities in finite-amplitude internal gravity waves

The parametric instability of a plane internal gravity wave is considered. When the two-dimensional equations of vorticity and mass conservation are linearized in the disturbance quantities, partial differential equations with periodic coefficients result. Substitution of a perturbation of the form dictated by Floquet theory into these equations yields compatibility conditions which, when evaluated numerically, give the curves of neutral stability and constant disturbance growth rate. These results reveal that, for an internal wave of even infinitesimal amplitude, disturbance waves can begin to grow in amplitude. Moreover, these parametric instabilities are shown to reduce to the classical case of the nonlinear resonant interaction in the limit of vanishingly small basic-state amplitude. The fact that these unstable disturbances can exist for an internal wave of any amplitude suggests that this phenomenon may be an important mechanism for extracting energy from an internal gravity wave.

The Propagation and Evolution of Cyclonic Gulf Stream Rings

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 maxU1 and maxU2 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 (U1 = U2) are weakly dispersive, propagating recognizably for long periods of time, and, nearly barotropic eddies (U1 ≈ U2) 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 (maxU1)/βl2. Both westward and northward speeds increase with incre...

The Generation and Evolution of Mushroom-like Vortices

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 alw...

Internal-Inertial Waves in a Surgasso Sea Front

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...

The Birth and Evolution of Eastward-Propagating Modons

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(−r2/2L2) 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 center...

Ocean Surface Currents From AVHRR Imagery: Comparison With Land-Based HF Radar Measurements

We focus on inverting the surface temperature (or heat) equation to obtain the surface velocity field in the coastal ocean and compare the results with those from the maximum cross correlation (MCC) technique and with the in situ velocity fields measured by the Rutgers University Coastal Ocean Dynamics Radar (CODAR). When compared with CODAR fields, velocities from the heat equation and MCC have comparable accuracies, but the heat equation technique better resolves the finer scale flow features. We use the results to directly calculate the surface divergence and vorticity. This is possible because we convert the traditionally underdetermined heat inversion problem to an overdetermined one without constraining the velocity field with divergence, vorticity, or energy statements. Because no a priori assumptions are made about the vorticity, it can be calculated directly from the velocity results. The derived vorticity field has typical open-ocean magnitudes ( ~ 5 times 10-5/s) and exhibits several structures (a warm core ring, Gulf Stream filament, and a diverging flow) consistent with the types of flows required to kinematically deform the sea surface temperature patterns into the observed configurations.

The July 1990 Gulf Stream Experiment

The specific scientific tasks addressed in the July 1990 Gulf Stream (GS) experiment were the following: (1) Kelvin wake behavior across fronts at various ship speeds, (2) the physics of temperature front/radar cross section (RCS) mismatch, (3) wave-current interactions in curvature fronts, and (4) the hydrodynamic structure and origin of synthetic-aperture-radar (SAR) slick-like features. Overall, the GS Experiment was most successful, and about 60 percent of the planned data was collected. On-going efforts concentrate on the analysis and interpretation of the data. An overview of the experiment and preliminary results of the data analysis are given.

Kinematics of a warm-core dipole ring

The remote sensing and in situ data used by Hooker and Brown (1994) to establish the dipole identity of warm core ring (WCR) 82-B is reexamined. It is found that a rotating barotropic modon (Mied et al., 1992) can be constructed with the same dipole rotation rate, center-to-center vortex separation distance, and peak anticyclonic vorticity as those of WCR 82-B. The model-derived velocity field is used to deform an array of material lines during a rotation period when the dipole is evident in the imagery and agreement between the model and the imagery is good. Specifically, it is observed that at the end of the imaging period, the surface tracer assumes a skewed dipole appearance, in which the line of centers is not perpendicular to the separatrix. Moreover, the separatrix morphology is qualitatively reproduced. Finally, the cyclone assumes an axisymmetric form. An attempt to derive qualitatively similar signatures using only monopole forcing yields results dissimilar from both the advanced very high resolution radiometer imagery and those obtained with the dipole, further confirming the underlying dipole character of WCR 82-B.

Longitudinal convergence fronts in homogeneous rotating channels

In situ observation and remote sensing imagery indicate the presence of velocity convergences located over bathymetric channels in the mouths of tidal estuaries. In this paper we present the results of numerical simulations performed to investigate these velocity structures in a rotating channel having a single bathymetric groove. The equations of motion for a homogeneous fluid on a rotating Earth are solved using a fully spectral code in the across-channel (i.e., the vertical or x-z) plane. No along-channel flow variations (in the y direction) are permitted. The bottom bathymetry is formed using a unique virtual surface approach [Goldstein et al., 1993] that generates a no-slip bottom using feedback forcing. A Gaussian-shaped channel is employed to simulate typical estuarine bathymetry. In the along-channel direction a constant pressure gradient is imposed, and the flow evolves until a steady state results. The simulations are performed at high Rossby number (of order unity) based on the width of the groove and a typical surface velocity. Simulations show the development of a localized along-channel jet colocated with an across-channel recirculation cell. This feature results from the generation of streamwise vorticity through the tilting of planetary vorticity by the vertical shear in the along-channel flow. The associated across-channel surface flow above the jet exhibits convergent and divergent regions, which correlate reasonably well with features reported previously in the literature. Their number, position, and strength are seen to vary with the along-channel Reynolds number, Ekman layer thickness, and channel aspect ratio.

Frontogenesis with ageostrophic vertical shears and horizontal density gradients: Gulf Stream meanders onto the continental shelf

This paper deals with frontogenesis in the presence of ageostrophic vertical current shears and horizontal density gradients. The problem has broad application to the situation encountered in tidal fronts and current system meanders, but specific focus here is on Gulf Stream meander crests and filaments that advance onto the continental shelf just north of Cape Hatteras. These occur typically every few days as Gulf Stream meanders progress northeastward through the South Atlantic Bight and past Cape Hatteras. We model the submesoscale evolution of the interface between the continental shelf water and these Gulf Stream features while they are on the continental shelf. We assume the region to be characterized by an initial condition consisting of a horizontal density transition region and an ageostrophic, surface-intensified horizontal flow. The ensuing frontogensis process is modeled numerically with an f plane calculation employing the full nonlinear equations in the depth/cross-front plane; flow is assumed out of this plane (along the front), but no variation of the flow in this direction is allowed. A pseudospectral model is employed using trigonometric functions in the horizontal and Chebyshev polynomials in the vertical. Many different scenarios are investigated by changing the width, shape, and relative positions of the density transition and velocity jet. In the majority of cases a propagating hydraulic jump is formed. Simultaneously, the initial surface jet evolves to a subsurface-intensified jet while it weakens and ultimately changes directions. The presence of this strong velocity jet can substantially enhance the rate of jump formation or completely inhibit frontogenesis. Supporting analytical calculations are used to show that the presence of vertical ageostrophic shear can augment or oppose the usual frontogenesis mechanism present when the collapsing horizontal density gradient is acted on by the resulting convergent surface current. The outcome of the shear/density gradient interaction depends upon the position of each field with respect to the other. In the vicinity of the nose of the hydraulic jump for the cases investigated, the density is seen to have a qualitatively similar dependence upon the stream function in the translating frame, irrespective of the initial condition from which it evolved.