Arnold L. Cooper

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.

Radar surface signatures for the two‐dimensional tidal circulation over Phelps Bank, Nantucket shoals: A comparison between theory and experiment

A comparison is made between real aperture radar (RAR) measurements and simulations (based on modeled tidal currents) of radar cross section over a complicated tidal basin (in the vicinity of the Phelps Bank region of the Nantucket shoals) in order to more fully understand the origin of radar signatures that are observed at the ocean surface as a consequence of variations in the topography of the ocean bottom. The Phelps Bank region was mapped under two extreme wind speed conditions: in high winds, in excess of 15 m/s, and in low winds, of the order of 2–3 m/s. For the light-wind case the measured radar cross section over the west side of the Phelps Bank was enhanced by as much as 20 dB relative to the clutter background. For the high-wind case, no discernible bathymetric signature was found in the highclutter background. Numerical results for the two-dimensional M2 (semidiurnal) tidal currents over the Phelps Bank (Greenberg et al., 1989), with ⅛ × ⅛ min of arc resolution, are used as input to the surface signature models: the Alpers and Hennings (1984) first-order Bragg relaxation model; a generalized form of this relaxation model (in which wind directional effects are incorporated in an approximate manner); and the full-spectrum model of Lyzenga and Bennett (1988). Comparisons between the models (which do not include wave breaking) and an extreme case of 2–3 m/s winds (where strong wave breaking could become important) reveal that although the models predict correlation between variations in bottom topography and surface signature, they significantly underpredict the magnitude of the observed effect. The model calculations also are very sensitive at low (<2 m/s) wind speeds to the functional form that is assumed for the wind-wave forcing in the wave action equation. Prior visual observations and measurements of wave spectra (and wave shoaling) in the vicinity of Phelps Bank strongly suggest that the deficiencies of the modeled results that occur explicitly at light winds are due to wave breaking. A number of additional experiments and measurements are suggested for more normal environmental conditions for further theory assessments.

Hydrodynamic Stability of a Rotating Liner.

The Rayleigh‐Taylor instability is investigated for a nonsteady basic state. A model of a magnetically imploded cylindrical metallic liner compressing an axial magnetic field is constructed and used as the basis of a linear stability analysis. The liner, idealized to be without energy loss mechanisms, can be given an initial rotation about its axis. Analytic and numerical techniques are used to study the stability of flutelike (∼eimφ) irrotational perturbations about this state. Stability is quantified in terms of the tendency of the liner to disrupt or to encroach toward the axis, and is determined as a function of mode number m, the form of initial disturbance, liner thickness and the amount of rotation. It is shown that thickening the liner tends to stabilize against both encroachment and disruption, while increasing rotational velocity tends to stabilize against encroachment. Implications for experimental designs are discussed, in particular for experiments with deep compressions (large ratio of initi...

Radar backscatter from breaking waves in Gulf Stream current convergence fronts

Bright linear features have been observed in radar imagery taken near the Gulf Stream (GS) boundary on two separate occasions. In each case, these have been observed directly over strong current convergences. Progress has been made in understanding the origin of these signatures through simulations that incorporate environmental forcing from the winds and currents. These simulations significantly underestimate the backscatter unless wave-breaking (WB) effects are included at least approximately. Using a new, quasistatistical procedure that generalizes and quantifies earlier procedures for including WB effects, the authors have been able to successfully simulate the magnitude and behavior of these signatures. The approach combines the statistically based, composite model of radar backscatter with a deterministic feature model that relates backscatter from breaking waves to a particular geometrical model of a spilling breaker. This is accomplished using localized criteria, defined by local wave crest acceleration, to determine the probability of breaking, and by extending the feature model so that its unknown parameters may be evaluated directly from wave-current interaction calculations. The new approach provides an estimate of the critical crest acceleration of a potentially breaking wave, as a function of wind speed, that agrees with independent measurements.

Vortex shedding due to laser ablation

An investigation of laser‐driven targets shows the generation and subsequent shedding of strong vortex structures from the ablation layer whenever the density and pressure profiles become noncollinear. It is shown here that vortex shedding explains the inhibited linear Rayleigh–Taylor growth, the short‐wavelength cutoff, dynamic stabilization and clarifies the role of the Kelvin–Helmholtz roll‐up.

Evolution of freely propagating, two‐dimensional surface gravity current fronts

This work addresses the two-dimensional propagation and shape evolution of surface gravity current fronts with a surface density outcrop frontal line. The problem is formulated using the reduced gravity shallow water equations, and the gravity currents are assumed to advance into a fluid at rest. We formulate a nonlinear analytical model for the gravity current plume front morphology by applying the shock tube theory of compressible fluids, which casts the problem in the form of an initial value calculation to be solved numerically. The simulations are initiated by assuming three different plan forms for the initial plume front and their subsequent evolutions followed in time. The paper is concerned exclusively with gravity current fronts having initially a uniform frontal propagation speed locally normal to the plume front, and a number of interesting results emerge. We find that an initially concave region of the front can lead to a nonlinear focusing that results in an energetic bulge in the frontal plan view. These bulges form sharp angles, or kinks, where they are joined to the front at their edges on either side. As they evolve, these angles increase toward 180° (a straight line), and the front becomes smoother in time. The orientation of the bulge and kink features predicted by the model is in agreement with visual and radar imagery observations. The kinks are always oriented toward the lighter plume material. When a plume has two or more such concave regions, the resulting energetic bulges can interact at a later time. The issue of determining plume speeds by tracking these features on sequential images of gravity currents is also dealt with.

Wave propagation along freely propagating surface gravity current fronts

This work deals with the propagation and evolution of disturbances which move along freely p opagating two-dimensional gravity current fronts. Examples of evolving perturbations on fronts are displayed in real-aperture radar images of gravity currents in the coastal zone. The theory of Cooper et al. (2001), which is based upon the ray tube formulation of Whitham (1974), is employed t simulate disturbances of the sort seen in this imagery and in the larger body of literature. Initial a omalies in both shape and velocity are introduced and allowed to evolve, and several types of new and interesting behaviors emerge. Shape perturbations of the form x = a sech δy evolve into two anomalies, which separate in time as they propagate in opposite directions along the front. When the value of a is increased, the disturbances, which propagate along the gravity current, can break, forming breaking frontal waves (BFWs). These manifest themselves as sharp angular features to either side of the main bulge. Two types of velocity disturbances are employed. The first has the form U = U 0 (1 + a sech δy), and evolves to preserve a single frontal bulge that increases in amplitude and width as it propagates. Here again, large values of â result in BFWs. In this case, they replicate the general behavior present in the imagery. The second type of velocity perturbation used is U = U 0 (1 + â cos δy). The smallest values of a generate no BFWs, but yield fronts which oscillate in space and time. Larger values produce a string of BFWs which are qualitatively similar tc the cusp-and-trough morphology observed so frequently in nature. The largest values of a allow the gravity current to form a string of large, bulbous structures which intersect one another as they propagate forward and spread laterally. And finally, we make an effort to correlate the results of the simulations with the shapes seen in radar and visible imagery in the literature.

Study of Gulf Stream features with a multifrequency polarimetric SAR from the Space Shuttle

Using simulations of radar cross section (RCS) based on wave-current interaction calculations, the authors investigate the origin of a prominent enhancement in L-band from signals that were transmitted and received, respectively, with horizontal (H) and vertical (V) polarization radar return. This was observed in imagery of the northern boundary of the Gulf Stream (GS) during the first Shuttle Radar Laboratory (SRL-1) mission. The calculations of surface roughness are based on a one-dimensional (1D) surface current model that closely resembles a current shear that was observed in in situ current measurements, taken at both sides of the GS at the time SRL-1 imaged the GS boundary. In agreement with trends observed in the imagery, significant enhancements in L-band HV polarization cross section occur in the neighborhood of the GS thermal boundary, relative to comparable vertical polarization (VV) cross section signatures at X-, C-, and L-band. The authors also find reasonably good agreement between the simulated and observed magnitudes of the GS signatures (based on calculations of wave action) using two different radar imaging models, and they provide an overview of a number of additional submesoscale features associated with the GS that were present in the image of the GS boundary.

Magnetic flux diffusion in imploding liquid liners

Calculations have been made of the rate at which confined magnetic flux compressed by an imploding cylindrical liquid metal liner diffuses into the latter because of finite electrical resistivity. The diffused magnetic field profile and associated magnetic energy and Joule heating are also calculated. In the limit of high magnetic Reynolds number Rm, the skin depth, total diffused flux, and associated energy scale like Rm−1/2. It is shown that cylindrical liner motion mitigates the diffusion calculated in slab models, owing to the reduction in the surface area through which the flux must diffuse. The influence of the form of the liner motion on the results is displayed.

On the origin of bright lines and other features in X-band radar imagery of frontal surface velocity fields

Enhanced radar backscatter occurs in radar imagery of strongly convergent ocean currents, but the origin of this phenomenon is not well-understood. Although the Alpers and Hennings (AH) relaxation model indicates that variations in radar cross-section (RCS) intensity at convergent fronts are proportional to the magnitude of the local current convergence, at higher radar frequencies, this model significantly underpredicts RCS enhancement and exhibits a non-physical look-angle dependence. Full-wave spectral modeling incorporating composite Bragg backscatter does not remedy the situation. In developing a procedure for extracting estimates of the near frontal 2-dimensional surface velocity fields of convergent ocean frontal features from radar imagery, the authors have identified a plausible explanation, empirically, that accounts for the correlation between the presence of bright lines in X-band radar imagery near convergent fronts and the magnitude of the local current convergence. The authors are able to quantitatively infer a 2-dimensional model of the currents, using radar data simulations of wave spectra, and radar cross-section RCS. In the resulting model, enhanced radar intensity occurs where the local convergence increases because of enhanced wave-steepening and wave-breaking. Other effects associated with current structure (for example, shear) are discussed.