Thomas E. Evans

Subsurface, surface, and radar modeling of a Gulf Stream current convergence

In this paper we investigate the underlying dynamics associated with a strong, line-shaped submesoscale feature that was observed in radar imagery at the boundary between Gulf Stream (GS) and shelf water near Cape Hatteras during the first Naval Research Laboratory High-Resolution Remote Sensing Experiment (HIRES 1). The line-shaped feature, which appears as a pronounced (∼10 dB) increase in radar cross section, extends several kilometers in the east-west direction. In situ current measurements have shown that this feature coincides with the boundary of a sharp current convergence front. These measurements also indicate that the frontal dynamics is associated with the subduction of denser GS water under lighter shelf water. Using the observation that the convergence can be attributed to a hydrodynamic instability at the water interface, we have modeled the resulting subsurface hydrodynamics on the basis of a rigid-lid, two-dimensional solution of the Navier Stokes equation. The calculations of subsurface current flow were used as input to a spectral (wave action) model of wave-current interaction to obtain the surface wave field, which in turn was used to provide input for modeling of radar backscatter. The resulting description also includes the effects of surfactant-induced wave damping on electromagnetic backscatter. Our predictions are compared with real aperture radar imagery and in situ measurements from the HIRES 1 experiment.

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.

Surface‐to‐subsurface velocity projection for shallow water currents

Sea surface currents in coastal oceans are accessible to continuous direct observations by shore-based high-frequency Doppler radar systems. Inferring current structure in shallow water from such surface current observations is attempted. The approach assumes frictionally dominated flow and vertically varying current velocity on the scale of the Ekman boundary layer. The approximation of the velocity variation with depth is consequently derivable in terms of orthogonal basis functions from the sea surface kinematic and dynamic boundary conditions; specifically, the viscous momentum and shear equations evaluated at the sea surface. The inference procedure developed is demonstrated with sea surface data obtained in the coastal High-Resolution Remote Sensing Experiment on the continental shelf off Cape Hatteras. Despite uncertainties in the surface measurements, qualitative agreement is obtained between the inferred subsurface current and the current measured in situ. The sensitivity of the inference to the measurement uncertainties as well as to the model assumptions is investigated, and the inferred result is found to be generally robust.

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.

Convergence fronts in tidally forced rotating estuaries

In situ observation and remote sensing imagery reveal the presence of longitudinal velocity convergences over bathymetric channels in tidal estuaries. We present the results of numerical experiments designed to investigate the cause of these convergences for channels possessing shallow shoal regions and a deeper central region. The equations of motion for a homogeneous fluid on a rotating Earth are solved using a fully spectral code in the across-estuary (i.e., the vertical or x-z) plane, while no along-estuary flow variations (in the y direction) are permitted. A Gaussian-shaped bottom bathymetry is chosen. In the along-channel (y) direction we impose a pressure gradient which is the sum of constant and fluctuating parts to simulate the steady and tidally oscillating parts of the estuarine flow. The details of the transient response can be complicated, but we observe that for most (∼80%) of the tidal cycle there exists a cross-estuary recirculation cell colocated with a localized along-channel jet. Both of these are situated over the bottom bathymetric groove; the circulation is always clockwise when facing down current. This feature results from the generation of stream-wise vorticity through the tilting of planetary vorticity by the vertical shear of the along-estuary flow. A surface convergence-divergence pair is associated with the flow. The maximum value of each is seen to occur on the edge of the bathymetric feature but may migrate toward or away from the center as long as the current continues in the same direction. When the tide reverses, the feature reappears on the opposite shoal, and the migration of the convergence and divergence extrema begins again. We also find that the responses are qualitatively similar for all bathymetric grooves, even asymmetrically situated ones, provided that the estuary width-to-depth ratio is of order 100 or larger, the Rossby numbers are of order unity, and the Ekman layer thickness-to-channel-depth ratio is greater than ∼0.65.

Inertial instability of large Rossby number horizontal shear flows in a thin homogeneous layer

A horizontal shear flow having a Rossby number, Ro, greater than unity on a rotating plane can become unstable when its shear value is less than −f, the Coriolis frequency. In this paper, this instability is investigated for an O(10 km) submesoscale, sinusoidal shear flow in a thin homogeneous fluid layer as in an oceanic mixed layer or a shallow sea. The most unstable mode is shown by a linear analysis to occur in a narrow localized region centered around the maximum anticyclonic current shear. However, nonlinear numerical calculations show that the instability can grow to encompass both unstable and stable regions of the current. A consequence of this finite-amplitude evolution is the formation of surface convergence/shear fronts. The possibility that inertial instability mechanism is a source of some surface convergence/shear features seen in remote sensing images of the sea surface is discussed. A comparison is made with the shear-flow instability that can occur concurrently in a sinusoidal shear current, and inertial instability is shown to be the dominant instability mechanism in the immediate range above Ro=2.

Polynomial Chaos Quantification of the Growth of Uncertainty Investigated with a Lorenz Model

Abstract A time-dependent physical model whose initial condition is only approximately known can predict the evolving physical state to only within certain error bounds. In the prediction of weather, as well as its ocean counterpart, quantifying this uncertainty or the predictability is of critical importance because such quantitative knowledge is needed to provide limits on the forecast accuracy. Monte Carlo simulation, the accepted standard for uncertainty determination, is impractical to apply to the atmospheric and ocean models, particularly in an operational setting, because of these models’ high degrees of freedom and computational demands. Instead, methods developed in the literature have relied on a limited ensemble of simulations, selected from initial errors that are likely to have grown the most at the forecast time. In this paper, the authors present an alternative approach, the polynomial chaos method, to the quantification of the growth of uncertainty. The method seeks to express the initial...

Acoustic propagation under tidally driven, stratified flow

Amplitude and phase variability in acoustic fields are simulated within a canonical shelf-break ocean environment using sound speed distributions computed from hydrodynamics. The submesoscale description of the space and time varying environment is physically consistent with tidal forcing of stratified flows over variable bathymetry and includes the generation, evolution and propagation of internal tides and solibores. For selected time periods, two-dimensional acoustic transmission examples are presented for which signal gain degradation is computed between 200 and 500 Hz on vertical arrays positioned both on the shelf and beyond the shelf break. Decorrelation of the field is dominated by the phase contribution and occurs over 2-3 min, with significant recorrelation often noted for selected frequency subbands. Detection range is also determined in this frequency band. Azimuth-time variations in the acoustic field are illustrated for 100 Hz sources by extending the acoustic simulations to three spatial dimensions. The azimuthal and temporal structure of both the depth-averaged transmission loss and temporal correlation of the acoustic fields under different environmental conditions are considered. Depth-averaged transmission loss varies up to 4 dB, depending on a combination of source depth, location relative to the slope and tidally induced volumetric changes in the sound speed distribution.

Sub-Mesoscale Modeling of Environmental Variability in a Shelf-Slope Region and the Effect on Acoustic Fluctuations

A coupled oceanographic/acoustic simulation model is under development for studying the relationship between acoustic field variability and dynamic oceanographic processes in a continental shelf/slope environment. The oceanographic component of the model involves numerical integration of the non-linear hydrodynamic equations of motion describing density, temperature and salinity distributions as a function of space and time. This component includes sub-mesoscale dynamics, allowing for the generation and propagation of non-hydrostatically generated phenomena such as tidally driven internal tides and solitary waves. Results are mapped into the corresponding sound speed distribution, and the resulting set of time evolved sound speed fields is used as input to a wide-angle parabolic equation that computes the acoustic field propagating through the environment. The general approach is discussed, and an illustrative result is presented that links acoustic field variability to specific oceanographic features.