Gloria J. Lindemann

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...

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.

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.

Rotating Modons over Isolated Topographic Features

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=ra. These conditions are imposed upon an isolated seamount or depression of the form η=h0[1−(r/rb)m] (and η=0 for r≥rb) with primary focus on the m=2 case. Two different scenarios result from this choice of topography and correspond to ra/rb=α½≥1 or α½≤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. Topographical...

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.

Symmetric baroclinic instability during frontogenesis with horizontal density gradients and ageostrophic vertical shears

This work examines the stability of surface frontogenesis in the presence of a horizontal density gradient and an ageostrophic current. We pose an initial value problem, in which two homogeneous bodies of water with different densities are separated by a horizontal transition region for the density. A surface current jet flows along the density front, and the geostrophic adjustment process is simulated using a fully nonlinear pseudo spectral numerical calculation in a 10 km × 30 m range and depth domain. We allow the evolution of the surface current jet but do not permit its variation in the y direction (perpendicular to the computational domain). A number of simulations are performed for a wide range of density differences and jet strengths. Surface frontogenesis and a tendency toward geostrophic adjustment of the initially ageostrophic fields do not always exhibit a smooth subsurface circulation accompanying the bunching of the surface isopycnals. Instead, a vortex is sometimes shed from the vicinity of the evolving front, and the isopycnals are distorted by this smaller-scale vortical flow. To determine the source of the secondary symmetric baroclinic instability, the acceleration potential of the individual terms in the vorticity equation is calculated. The instability is caused by the vertical shear in the along-front jet, which is intensified by the advection and vortex-tilting processes during the frontogenesis. Although this vortex is left behind by the propagating hydraulic jump, it subsequently matures into a secondary hydraulic jump on its own. We found that in marginally unstable cases an increase in the kinematic viscosity can suppress its occurrence. Finally, we show that the unstable vortex is separate and distinct from the captured turbulent rotor which is thought to be locally trapped at a location just behind the propagating front.