Doron Nof

The translation of isolated cold eddies on a sloping bottom

A two-layer analytical model is considered to examine the dynamics of cold isolated patches on the ocean floor. Such patches have been observed in the North Atlantic Ocean and are characterized by a bounding interface that intersects the bottom along a closed curve. They correspond, therefore, to isolated anticyclonic eddies with a lens-like cross section. The model incorporates steady movements resulting from the swirl velocity within the eddy and a topographically-induced translation. The movements are assumed to be frictionless and nondiffusive but are not restricted to be quasigeostrophic in the sense that the Rossby number is not necessarily small. For steady motions, analytical solutions are obtained using the full equations of motion in a coordinate system moving with the eddy itself. A uniformly sloping bottom causes a steady translation at 90° to the right of the downhill direction. Thus, the model predicts that an anticyclonic eddy on the ocean floor will migrate along lines of constant depth. Suprisingly, the predicted translation speed depends only on the gravitational acceleration, the density difference between the layers, the Coriolis parameter, and the bottom slope. It is independent of the intensity, size, and depth of the eddy. For the range of parameters typical for the deep ocean, the predicted translation speed is 5 to 10 cm s−1. It is estimated that isolated eddies on the ocean floor may be able to carry temperature anomalies for a few thousand kilometers away from their origin.

On the β-Induced Movement of Isolated Baroclinic Eddies

Abstract In this paper an analytical method is proposed for calculating the nonlinear β-induced translation of isolated baroclinic eddies. The study focuses on frictionless anticyclonic eddies with a uniform anomalous density and a lens-like cross section which translates steadily in a resting Ocean. The depth of these eddies vanishes along the outer edge so that as they translate westward their entire mass anomaly is caused along with them. The proposed method for calculating the translation speed incorporates the nonlinear equations of motion in an integrated form and a simple perturbation scheme. It relates the translation of the eddy to its intensity, size and volume, but requires only an approximate knowledge of the corresponding numerical values. The power and usefulness of the proposed method is demonstrated by its application to a class of simply-structured eddies whose swirl velocity increases monotonically with the distance from the center. It is found that the translation of these eddies is con...

The Ballooning of Outflows

Abstract It has been recently shown that when an inviscid outflow empties into the ocean, a steady alongshore current (in the Kelvin wave sense) cannot be established. This is due to the impossibility of balancing the alongshore momentum flux. To offset this momentum-flux deficit the outflow balloons near its source, forming an anticyclonic bulge. Using 1½-layer analytical and numerical models, the authors show that, on an f plane, the Coriolis force associated with the offshore movement of the growing bulge (which pushes itself away from the wall) compensates for the momentum flux of the longshore current downstream. With the aid of the slowly varying approximation, an inviscid nonlinear analytical solution is constructed. Numerical simulations with the Bleck and Boudra model are also performed. It is found that an outflow with an intense anticyclonic vorticity (i.e., a zero potential vorticity outflow with a relative vorticity of −f) produces a steep gyre that balloons (i.e., its radius increases with t...

Why Are There Agulhas Rings

Abstract The recently proposed analytical theory of Nof and Pichevin describing the intimate relationship between retroflecting currents and the production of rings is examined numerically and applied to the Agulhas Current. Using a reduced-gravity 1½-layer primitive equation model of the Bleck and Boudra type the authors show that, as the theory suggests, the generation of rings from a retroflecting current is inevitable. The generation of rings is not due to an instability associated with the breakdown of a known steady solution but rather is due to the zonal momentum flux (i.e., flow force) of the Agulhas jet that curves back on itself. Numerical experiments demonstrate that, to compensate for this flow force, several rings are produced each year. Since the slowly drifting rings need to balance the entire flow force of the retroflecting jet, their length scale is considerably larger than the Rossby radius; that is, their scale is greater than that of their classical counterparts produced by instability...

The Squeezing of Eddies through Gaps

Abstract The islands of the Lesser Antilles present a porous meridional barrier to North Brazil Current (NBC) rings. To better understand if, when, and how a NBC ring could be squeezed into the Caribbean Sea through such a gappy barrier, the encounter of a westward drifting eddy with a porous meridional wall is considered. First an eddy encountering a single aperture is modeled. To do so, both an analytical model and a reduced-gravity primitive equations numerical model are used. This was followed by numerical experiments that explored eddy collisions with barriers containing many gaps. In all of these models, the collisions were forced by either β or a steady advection through the gap(s). Using integrated constraints, an analytical solution was constructed for a zero potential vorticity lens passing through a single gap on a β plane. The solution involves a small parameter e, the ratio of the short timescale associated with the f-plane adjustment, and the long encounter timescale due to β. It is found th...

The Exhaust Valve of the North Atlantic

During glacial periods, climate records are marked by large-amplitude oscillations believed to be a result of North Atlantic (NA) freshwater anomalies, which weakened the thermohaline circulation (THC) and introduced instabilities. Such oscillations are absent from the present interglacial period. With the aid of a semiglobal analytical model, it is proposed that the Bering Strait (BS) acts like an exhaust valve for the above NA freshwater anomalies. Specifically, it is suggested that large instabilities in the THC are only possible during glacial periods because, during these periods, the BS is closed. During interglacial periods (when the BS, the exhaust valve, is open), low-salinity anomalies are quickly flushed out of the North Atlantic by the strong Southern Ocean winds.

The Momentum Imbalance Paradox Revisited

Abstract The classical problem of a point source situated along a southern boundary emptying buoyant water into a (β plane) ocean is revisited. Pichevin and Nof (PN) have shown that, in contrast to the view prevailing at the time, such an inviscid outflow does not simply turn to the right. Rather, it bifurcates into two branches: a steady branch that does turn to the right (eastward) and an unsteady branch that periodically sheds eddies to the left (westward). This partition is because a simple turn to the right of the entire outflow leaves the outflow’s long-shore momentum flux unbalanced, creating a paradox. In contrast, the branching allows the westward-drifting eddies (westward branch) to balance the momentum flux of the steady current (eastward branch). Although the analytical PN solution is useful and informative, it is cumbersome and difficult to apply to actual outflows. Here, a considerably simpler nonlinear analytical solution is presented. Using the idea that the eddies grow slowly relative to ...

Collision and separation of boundary currents

The collision and separation of two opposing boundary currents is investigated with simple inviscid, barotropic and baroclinic models on an f-plane. The underlying hypothesis is that currents originally set in the oceanic interior turn into jets that flow along a coast until they ultimately collide. At the confluence zone both currents turn seaward; our aim is to compute the speed, width and veering angle (i.e. the angle between coast and the axis of offshore jet) of the merged offshore currents. Steady solutions are obtained analytically by considering the conservation of potential vorticity, the Bernoulli integral and the integrated constraints associated with conservation of mass and momentum. In the purely barotropic case the currents turn offshore when they reach the stagnation point, resulting from the collision. It is found that the velocities of the two approaching jets at the coast (y = 0) need to be identical in order for a stationary steady to be reached. When this “balance” condition is not met, the entire system of separated currents drifts along the wall toward the weak current. For the more complicated (and realistic) baroclinic cases, we consider a 112-layer (consisting of one active layer and an infinitely deep inactive layer) and 212-layer system (consisting of two active layers and an infinitely deep inactive layer). For simplicity, one jet is assumed to have zero potential vorticity, whereas for the other jet the potential vorticity is taken to be uniform. The relation between the depth of the approaching jets at the coast and the veering angle is computed for both cases. As in the barotropic case, both baroclinic cases show that stationary steady solutions exist only for specific currents. It is expected that when the particular computed relationship between the two currents does not exist (i.e. the currents are unbalanced) the entire separated system will again drift along the wall. An alternative possibility is that the upstream conditions will somehow be altered until the stationary balance is obtained. These results suggest that separation of the western boundary currents can occur even without the β-effect or a vanishing wind stress curl over the ocean interior. The new separation process discussed above is due to the momentum imparted on the poleward flowing currents by the opposing flows. Possible application of this theory to the western boundary currents system in the South Atlantic is discussed.

The retroflection paradox

Abstract The classical question of what happens; when a warm western boundary current, such as the North Brazil Current (NBC), retroflects is addressed analytically using a reduced-gravity nonlinear model. The traditional view is that the northwestward flowing current separates from the wall, turns to the right (looking offshore), and forms a zonal boundary current that flows eastward. Integration of the steady inviscid momentum equation along the boundary gives the longshore momentum flux (or flow force) and shows that such a scenario leads to a paradox. To resolve the paradox the separated current must constantly shed anticyclones, which propagate to the northwest due to β and an interaction with the boundary. This new eddy shedding mechanism, which is not related to the traditional instability of a zonal jet, may explain why the NBC must produce rings. A nonlinear analytical solution to the problem is constructed with the aid of a powerful theoretical approach based on the idea that nonlinear periodic ...

On Geostrophic Adjustment in Sea Straits and Wide Estuaries: Theory and Laboratory Experiments. Part I: One-Layer System

Abstract The dynamics of outflows from sea straits and wide estuaries are examined through a simplified frictionless model whose primary motions are not constrained to be quasi-geostrophic. The potential vorticity equation is solved by means of approximate analytical methods. Some of the model predictions are tested in the laboratory. The mathematical model predicts that an outflow from a channel with uniform velocity distribution deflects to the right or left depending on the depth of the basin into which it debouches. There is a “critical” Rossby number below which the flow separates from one of the basin banks. When a non-uniform velocity is introduced upstream the direction of deflection may differ substantially from the upstream uniform flow case. The model shows that rotation is important whenever the ratio between the relative depth variation to the Rossby number is not negligible; rotational effects can be important even if the ratio between the channel width and the Rossby deformation radius is e...