Colin Y. Shen

The evolution of the double‐diffusive instability: Salt fingers

The finite‐amplitude growth of finger convection at an interface of two uniform solutions is studied to determine the processes that govern the scale and amplitude of the convection, the growth of the fingering interface, and the transition of the convection to turbulence. A conceptual model of fingering processes is provided and details are studied by means of direct numerical simulation. The simulations obtain full finger convection and turbulence for ratios of viscosity to diffusivities in the range between 1 and 10. The study shows that the evolution of finger convection in its entirety is characterized by the scale and amplitude of the fastest growing finger mode. In the parameter range studied, the growth of the fingering interface is found to be controlled mostly by molecular diffusion. Convective flux divergence only plays a secondary role. The growth of the interface is shown to have the effect of increasing the horizontal scale of the convection while decreasing the buoyancy flux. However, the k...

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...

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.

Heat‐salt finger fluxes across a density interface

The heat and salt fluxes produced by salt fingering at a density interface are studied with a numerical and an analytical model. Specifically, the issue concerning the value of the heat‐to‐salt flux ratio is addressed. The numerical modeling based on direct numerical computation of the nonlinear governing equations obtains values around 0.5. This value is approximately the average of widely varying experimental values reported in the literature. The large difference between the theoretical flux ratio predicted based on the buoyancy maximization hypothesis and the experimentally derived flux ratio is examined with an analytical model, which includes both effects of salt stratification in the interface and salt discontinuity at the edges of the interface. Combined with the numerical model results, the analysis shows that the disagreement can be traced to the flux maximization hypothesis itself. An alternative hypothesis that maximizes convective velocity amplitude is presented which gives flux‐ratio predict...

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.

An occluded coastal oceanic front

Field observations, including hydrographic, microwave imaging radar, and HF radar measurements, reveal the evolution of a complicated frontal interaction between three water masses on the continental shelf near Cape Hatteras, North Carolina, during a period of incursion of water from the Gulf Stream. The water masses were found to be separated by intersecting frontal lines configured in a manner analogous to an occluded atmospheric front. The densest water lay between inshore and offshore fronts that gradually merged or occluded in the generally downstream direction, leaving a single surface front. The overall frontal structure appeared as a distinct Y-shaped feature in the radar imagery, similar to historical imagery of the study area. The interpretation of the observations is aided by the use of a two-dimensional numerical model. The model is initialized with two fronts idealized from the ocean measurements. The model fronts quickly sharpen and begin to move together, eventually occluding into a single surface front. As a result of the occlusion, the water mass having intermediate density subducts and intrudes under the most buoyant water, carrying with it strong horizontal and vertical shears, and a frontal band of diverging currents is created in the densest water mass. The model thus suggests that in the ocean there will be an increase in hydrographic and velocity fine structure downstream of the frontal occlusion point.

NOTES AND CORRESPONDENCE Constituent Boussinesq Equations for Waves and Currents

Abstract The Boussinesq long-wave equations in constituent form are generalized to encompass both the irrotational long-wave dynamics and the rotational current dynamics. For irrotational long waves, the generalized equations are shown to represent both the weakly nonlinear and fully nonlinear Boussinesq-type wave equations given previously in the literature. The generalized equations are of additional interest in that they are effectively model equations for a weakly nonhydrostatic wave/current system, in which the conventional hydrostatic ocean current/wave model is a limiting case. The derived equations are related to the surface flow variables that are accessible to synoptic surface wave/current measurements such as those available from radar remote sensing.

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.

Scale transition of double-diffusive finger cells

The processes that bring about the change of cell size in the evolution of salt‐finger convection are investigated with a numerical model of the convection in a Hele–Shaw cell. It is shown that the increase of cell width during the convection is produced by the vertical penetration of increasingly wider cells from the edges of the finger zone into the interior, as has been observed in a laboratory experiment. The increase of scale is also shown to occur through the merging process in which narrow finger cells merge to form wider cells. Occasionally, transition from wide to narrow scale can occur, in which case the wide finger cell splits to form two or more narrow cells. The scale transition produced by the merging, penetration, and splitting processes is shown to have the effect of maximizing the buoyancy flux generation in an evolving finger convection. This maximization is also interpreted in terms of the most rapidly growing finger mode. The effect of the scale transition on the actual magnitude of th...