Lens-like Eddies Research Articles

Giant ice rings in southern Baikal: multi-satellite data help to study ice cover dynamics and eddies under ice

Abstract. Ice cover on lakes is subject to atmospheric forcing from above and the influence of water dynamics and heat flux from below. One characteristic example of these influences in some large lakes, such as Lake Baikal in Russia, are the giant ice rings and the associated eddies under the ice cover. In April 2020 a giant ice ring appeared in southern Baikal, and a lens-like eddy was detected below the ice. We analysed the temporal changes of ice cover using satellite images from multiple satellite missions – MODIS on Terra and Aqua, Sentinel-1 SAR, Sentinel 2 MSI, Landsat 8, PlanetScope, satellite photography from the International Space Station, and radar altimetry data from Jason-3. Satellite imagery and meteorological data show unusual temporal changes of ice colour in April 2020, which were explained by water infiltration into the ice followed by the competing influences of cold air from above and the warm eddy below the ice. Tracking of ice floe displacement also makes it possible to estimate eddy currents and their influence on the upper water layer. Multi-satellite data contribute to a better understanding of the development of ice cover in the presence of eddies, the role of eddies in horizontal and vertical heat and mass exchange, and their impact on the chemistry and biology of the lakes and on human activity.

Vozdeystviye mezomasshtabnoy vikhrevoy dinamiki na bioproduktivnost' morskikh ekosistem (obzor)

Different types of mesoscale eddy dynamics are considered in the paper from the viewpoint of their effect on the plankton (mainly phytoplankton) amount and its taxonomic structure. The eddy structures of all types, including cyclonic, anticyclonic, water-body anticyclonic and frontal ones, as well as the dipole structures, actively affect plankton. Theoretical schemes of the influencing mechanisms, which are illustrated by the examples of such an impact on the plankton in the Black Sea, are examined. The analyzed responses of the marine plankton ecosystems to the eddy dynamics and the scientific literature review unambiguously testify the important role of these processes in formation of biological productivity in the seas and oceans. Thus, a cyclonic eddy forms the isopycn rise (a domelike bend) in its core both in the thermocline and in the pycno-halocline that elevates nitrocline; it promotes bioproductivity increase. Whereas in the anticyclonic eddy core, the thermocline and pycno-halocline lowering (deflection) takes place; it negatively affects bioproductivity. At that, the isopycn rise occurs at the eddy periphery that, on the contrary, contributes to increase in primary production. In contrast to a conventional anticyclone, a lens-like eddy forms the water rise exceeding the maximum velocity horizon, in other words, in its upper part it often acts like a cyclone. Thus, in any gyre there are the areas where the thermocline rises to the surface and, therefore, the prerequisites for the bioproductivity increase are formed. Strong winds not only enhance the affect of the eddies on biota, but can completely change the nature of this impact. When exposed to wind, the rate of entry of the biogenic elements to the photic layer in the cyclones can decrease, whereas in the lens-like anticyclones it can increase. The important point is that the long-living eddies change the influencing mech-anisms depending on the stage of their evolution. At last, the eddy structures often promote changing in the dominant phytoplankton species that can significantly alter the flow of organic matter to the bottom and affect the global carbon cycle.

Eddy-Train Encounters with a Continental Boundary: A South Atlantic Case Study

Abstract Satellite altimetry suggests that large anticyclonic eddies (rings) originating from the Agulhas Current retroflection occasionally make their way across the entire South Atlantic Ocean. What happens when these rings encounter a western boundary current? In this work, interactions between a “train” of nonlinear lens-like eddies and a Southern Hemisphere continental boundary are investigated analytically and numerically on a β plane. The train of eddies is modeled as a steady double-frontal zonal current with the same vorticity and transport as the eddies themselves. The continental boundary is represented by a vertical wall, which is purely meridional in one case and is tilted with respect to the north in another case. It is demonstrated analytically that the eddy–wall encounter produces an equatorward flow parallel to the continental wall, thus suggesting a weakening of the transport of the associated (poleward flowing) western boundary current upstream of the encounter zone and unchanged transport downstream. A large stationary eddy is established in the contact zone because its β-induced force is necessary to balance the other forces along the wall. The size of this eddy is directly proportional to the transport of the eddy train and the meridional tilt of the wall. These scenarios are in good agreement with results obtained numerically using an isopycnal Bleck and Boudra model.

Deep, cross-equatorial eddies

The question of how deep ocean eddies can cross the equator is addressed with the aid of analytical and numerical models. We focus on the possibility that deep ocean (lens-like) eddies can cross the equator via deep cross equatorial channels on the ocean floor. We first examine the behavior of solid balls (i.e., free particles) in a meridional parabolic channel on a β plane. Such balls are subject to similar topographical forcing and inertial forces that a lens is subject to, except that pressure forces and friction are absent. We examine both single isolated balls and a “cloud” of (noninteractive) balls. In general, the balls' trajectories have a chaotic character; a fraction of the cloud crosses the equator and ends up in the northern hemisphere, and a fraction is left behind. More realistic numerical experiments (with a fully nonlinear reduced-gravity isopycnic model of the Bleck and Boudra type) show similar behavior. In all cases the equator acts as an “eddy smasher” in the sense that it breaks the lens into at least two parts, one crosses the equator and ends up in the northern hemisphere, and the other is left behind. Here, however, the system is not chaotic. Despite the obvious differences between clouds of balls and eddies, there is a remarkable similarity between the percentage of balls that penetrate into the opposite hemisphere and the percentage of eddies' mass that ends up in the other hemisphere. This suggests that the geometry of the channel and the presence of the equator determine how the fluid will be partitioned among the two hemispheres.

On the Westward Translation of Isolated Eddies

Abstract This paper examines the motion of an isolated lenslike eddy using the reduced-gravity shallow-water equations (SWE) on a β plane. In contrast to previous studies the author uses a correct first-order β-plane approximation of the SWE that posseses the same integrals of motion as the original system. The approximation includes terms proportional to (1 − y tanθ0/r0)−1, where y is the northward coordinate, θ0 the reference latitude, and r0 the earth’s mean radius. The center of mass of the eddy is found to oscillate meridionally and zonally with the inertial frequency f0 and drift westward at the same speed as in the case of the conventional β-plane approximation. The new terms arising from the non-Cartesian metric cancel each other. Therefore, the ad hoc procedure of replacing f0 by f0 + βy in the f-plane shallow-water equations does give the correct answer for the bulk motion of the eddy.

The Propagation of Submesoscale Coherent Vortices

Abstract A combined analytical and numerical examination of submesoscale coherent vortex (SCV) dynamics and propagation is conducted. This study is prompted by observations of the movement relative to their surroundings of one class of SCVs, that is, Meddies. An asymptotic analysis is performed to study the mechanics governing SCV propagation. It is found that the large-scale flow plays a dominant role in determining the trajectory of SCVs and that the β effect and form drag of neighboring layers are weaker effects. As a result, SCVs propagate at a speed that is a density-weighted average of the flow in the surrounding layers. Meddies may thus move relative to the surrounding water, which is in accordance with observations. This theory extends previous studies on eddy propagation by considering more general situations. For example, a lenslike eddy embedded in a nonzonal, vertically and horizontally sheared flow is studied. A significant difference between this study and most previous related work is that ...

Alignment of lenses: laboratory and numerical experiments

This paper addresses the question of what happens when two anticyclonic lens-like eddies with different densities come in contact with each other by, say, an advective current. We use laboratory and numerical experiments to demonstrate that, in a similar fashion to lenses with identical densities which often merge, lenses with unequal densities often align (i.e. the lenses “strive” toward a state where one lens is situated on top of the other). The two initially isolated eddies are formed in the laboratory by continuously injecting salty water through small filters situated in the interface separating two environmental layers. Hence, there is a total of four different fluids with graduated densities in the tank. The heaviest water is the lowest layer. One of the lenses is slightly lighter than this heaviest water and the other is still lighter than the first lens. Finally, the upper layer is the lighest of the four. Since the lenses are formed by injection, weak anticyclones which extend beyond the boundary of the lenses are formed above and below the lenses. Due to the continuous injection of fluid into the lenses they grow slowly so that after some time their edges meet. As in merging of lenses with identical densities, arms are then extended from one vortex to the other. However, in the present case the arms are situated above the heavier vortex and below the lighter vortex instead of being at the same level. At this point, the lenses are locked together and the arms continue to propagate and grow until the lenses ultimately align. This process is accompanied by filamentation where fluid is expelled from both lenses to accommodate the change in angular momentum. Comparable numerical experiments also are discussed. Here Gaussian lenses in a four-layer fluid are studied; the lenses occupy the two intermediate layers. The physical parameters of these experiments are chosen to resemble the now famous case of observed eddy merging off East Australia. In contrast to the laboratory study, the numerical lenses have no initial anticyclones located in the layers surrounding them. The results indicate alignment in a manner similar to the laboratory experiments, provided the eddies are initially sufficiently close.

Lenses generated by intermittent currents

A nonlinear mechanism for the generation of anticyclonic lens-like eddies from boundary currents is proposed. In contrast to the familiar generation processes that rely on unstable long waves that grow and close upon themselves or vortex shedding due to the geometry of the boundary, the present mechanism is related to intermittency in the current's mass transport. The essence of the new mechanism is that intermittencies in the transport (such as those in the Denmark Strait or the Mediterranean outflow) lead to unbalanced patches of fluid which break up into a discrete sets of eddies that interact with the boundary. The process is highly nonlinear because both the amplitude and the Rossby number are of order unity. It is modeled as follows: we begin with a rectangular box containing the motionless (light) fluid near the boundary. At, say, t = 0, the conceptual box is removed the unbalanced fluid undergoes two main processes. The first involves the establishment of a set of eddies via breakup and geostrophic adjustment, whereas the second is associated with the interaction of the set with the wall. These two processes are examined independently even though in reality the processes are, obviously, taking place at the same time. To examine the first processes we consider the nonlinear collapse of a (light) rectangular box in the open ocean away from the boundary. The breakup processes involves, of course, some sort of instability (because the patch does not remain intact) but this is not necessarily related to the long wave instability that is usually associated with long gravity currents. The general structures of the resulting final chain of eddies can be computed analytically by using the usual connecting principles, the conservation of potential vorticity and mass. It turns out, however, that the number of eddies and their detailed structure cannot be computed unless one invokes an additional constraint. To resolve this closure difficulty, the integrated angular momentum constraint, which is rarely used in oceanographic modelling, has been applied. The details of the second process (i.e. chain-wall interaction) are examined with the aid of the (above) results for the chained offshore eddies and the single eddy-wall interaction analysis of Nof (1988, Journal of Marine Research, 46, 527dash555). A combination of these two studies shows that a chain of lens-like eddies forced against a wall would leak fluid until all the eddies in the chain are merely ‘kissing’ the wall. Simple qualitative laboratory experiments on a rotating table support the conclusion that intermittencies in the current's transport lead to a group of eddies that leak along the wall. Such a group is formed even if the equivalent steady current is stable to long wave perturbation, i.e. the laboratory current would not have broken up had it not been terminating shoprlty after its formation. It is suggested that the observed mid-Atlantic eddies resulting fromt he Mediterranean outflow (Meddies) might be formed by a mechanism similar to our newly suggested process.

On the Cylinder Collapse Problem, Mixing, and the Merger of Isolated Eddies

Abstract The Rossby adjustment of an initially circular column of water, the so-called collapse of a cylinder, continues to be a widely used method for forming lenslike eddies in the laboratory. Here, we consider the structure of an eddy so formed as well as some ramifications of that formation. We demonstrate that the calculation of the eddy structure can be reduced to the extraction of the roots of two nonlinear, coupled algebraic equations. Analytical solutions in the limit of the collapse of a needle are given and roots are obtained numerically otherwise. It is concluded that in the collapse of a cylinder initially spanning the entire column of water, the eddy always maintains contact with both surfaces. (This is not the case in the seemingly equivalent two-dimensional case with no variation in one Cartesian direction.) In the event the initial cold column is separated only slightly from the surface, the above solution acts as the lowest order solution in a regular perturbation sequence. Next, these “...

The Fusion of Isolated Nonlinear Eddies

Abstract The interaction of two isolated lens-like eddies is examined with the aid of an inviscid nonlinear model. The barotropic layer in which the lenses are embedded is infinitely deep so that there is no interaction between the eddies unless their edges touch each other. It is assumed that the latter is brought about by a mean flow which relaxes after pushing the eddies against each other and forming a “figure 8” structure. Using qualitative arguments (based on continuity and conservation of energy along the eddies’ edge) it is shown that, once a “figure 8” shape is established, intrusions along the eddies’ peripheries are generated. These intrusions resemble “arms” or “tentacles” and their structure gives the impression that one vortex is “hugging” the other. As time goes on the tentacles become longer and longer and, ultimately, the eddies are entirely converted into very long spiral-like tentacles. These spiraled tentacles are adjacent to each other so that the final result is a single vortex conta...

Laboratory Experiments on the Merging of Nonlinear Anticyclonic Eddies

Abstract The mutual interaction of two isolated lenslike eddies is examined with the aid of a laboratory experiment on a rotating table. The isolated anticyclonic eddies are formed by withdrawing two cylinders containing a mixture of Freon (with a density of 1.53 gm cm−3), and silicone oil (with a density of 0.853 gm cm−3). The cylinders are embedded in water, and the collapse of the mixture forces two identical lenslike eddies (with an anticyclonic circulation) on the bottom of the tank. Initially, the lenslike eddies are completely separated from each other so that one vortex does not “know” about the presence of the other. Due to small bottom friction, the vortices spin down slowly so that after some time their edges meet and they touch each other, forming a “figure 8” structure. After this happens there is a rapid (i.e., within 20 revolutions) interleaving of the two eddies. Arms are extended from one vortex to the other and the vortices become one unit consisting of two main lenses. As the interactio...

Joint Vortices, Eastward Propagating Eddies and Migratory Taylor Columns

The behavior of an isolated pair of vortices consisting of two eddies situated on top of each other in a three-layer ocean is examined analytically. The amplitudes of both eddies are high and, consequently, the two eddies behave as one unit and migrate together in the ocean. For this reason, it is proposed to call the system joint vortices. The eddies are of equal or opposite sign; each vortex is situated in a different layer so that there are two active layers and one passive layer. Attention is focused on the behavior of joint vortices on a sloping bottom in the deep ocean and on a β plane in the upper ocean. That is, we consider deep joint eddies situated on an inclined floor in the lowest two layers of a three-layer ocean and upper joint eddies in the upper two layers. Special attention is given to the cases where one of the vortices is a lens-like eddy. Approximate solutions for slope (or β) induced drifts in the east-west direction are obtained. It is found that because of the high amplitudes and the resulting nonlinear coupling, the joint eddies have a mutual drift which is very different from the drift that each individual vortex would have. For example, while each individual vortex translates to the west in the absence of a conjugate vortex, the combined vortices may drift steadily to the east. This bizarre behavior stems from the presence of a “planetary lift” which is the oceanic equivalent of the side pressure force associated with the so-called Magnus effect. It is directed at 90° to the left of the drifting eddies. Other results of interest are: (i) Under some conditions, the westward drift of joint eddies consisting of two cyclonic vortices it much faster than the long-wave speed. Such fag drift contradict previously held contentions that the speed of cyclonic eddies cannot exceed the long wave speed. (ii) As it translates westward, an anticyclonic lens-like eddy can carry a Taylor column on top of it. Possible application of this theory to various eddies in the ocean is discussed.

On the ellipticity of isolated anticyclonic eddies

A simplified two-layer model is considered in order to describe the behavior of anticyclonic lens-like eddies embedded in a horizontally sheared flow. Attention is focused on light eddies (such as warm-core gulf stream rings) embedded in an infinitely deep fluid whose speed varies linearly in the horizontal direction. Non-linear solutions are constructed analytically using a power series expansion. It is found that a lens-like eddy embedded in a horizontally sheared flow, on an f plane, migrates at the average speed of the mean flow. As a result of the shear, the ring's shape is an ellipsoid whose orientation depends on the environmental flow. When the environmental shear is cyclonic, the ellipse is oriented perpendicular to the mean flow, and when the environmental shear is anticyclonic, the ellipse orientation is parallel to the mean flow. Although the ring migrates at a speed which differs from the speed of most of the surrounding fluid, the elliptical shape is fixed so that the whole eddy does not rotate due to the shear. A possible application of this theory to the warm-core rings found north of the gulf stream is discussed. DOI: 10.1111/j.1600-0870.1985.tb00271.x

Oscillatory drift of deep cold eddies

This paper supplements an earlier one on the dynamics of cold isolated eddies situated on a sloping oceanic floor ( Nof, 1983a, Deep-Sea Research, 29, 171–182). The lens-like eddies under investigation correspond to cold patches bounded by an interface that intersects the slopping floor along a closed curve. A wide range of possible time-dependent migration patterns is explored analytically. Nonlinear solutions are constructed by separating the equations governing the migration from those governing the eddy's interior. It is shown that, in addition to the known steady migration at 90° to the right of the downhill direction discussed previously, oscillatory migration is also possible. This time-dependent migration corresponds to a nonlinear eddy that drifts along a cycloid. The asymmetrical oscillations are of the inertial period. They are superimposed on a main migration path which, as in the steady migration case, is directed along a straight line whose orientation is at 90° to the right of the downhill slope. To an observer riding with the eddy, the circulation within the eddy appears to be steady whereas the migration is time dependent. As in the steady translation case, the drift is entirely independent of the eddy's size, intensity, and depth. It depends only on the density difference between the eddy and the environment, the gravitational acceleration, the bottom slope, and the Coriolis parameter. Application of this theory to various eddies situated on the ocean floor is discussed.

On the Interaction between Thin Isolated Eddies and Longshore Currents

Abstract A simplified two-layer analytical model describing the interaction between a longshore current and a thin lenslike eddy is considered. The eddy is situated near a vertical wall and is embedded in a frictional boundary current which is flowing from one latitude to another. Attention is focused on the conditions under which the boundary current compensates for the tendency of the eddy is drift due to β so that the eddy is stationary. The model incorporates movements resulting from the circulation within the eddy, the longshore flow and β. Both the upper and lower layer are taken to be active; diffusion is neglected but bottom friction is included. Although our model is simplified, the movements within the eddy are not constrained to be quasi-geostrophic, in the sense that the Rossby number can be relatively large and the interface surfaces at a finite distance from the center. The desired solutions are constructed analytically. It is found that a thin lenslike eddy adjacent to a western boundary ca...