Thierry Pichevin

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 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 ...

“Teddies” and the Origin of the Leeuwin Current

Abstract The outflow from the Indonesian seas empties approximately 5–7 Sv of surface warm (and low salinity) Indonesian Throughflow water into the southern Indian Ocean (at roughly 12°S). Using a nonlinear 1½-layer model with a simple geometry consisting of a point source (of anomalous water) situated along a meridional wall on a β plane, the spreading of these waters is examined. An analytical solution is constructed with the aid of the “slowly varying” approach, and process-oriented numerical simulations are performed. It is found that, immediately after emptying into the ocean, the outflow splits into two branches. One branch carries approximately 13% of the source mass flux and forms a chain of high amplitude anticyclonic eddies (lenses) immediately to the west of the source. These eddies drift westward and penetrate into the interior of the Indian Ocean. The second branch carries the remaining 87% of the mass flux via a coastal southward flowing current. Ultimately, this second branch separates from...

The Establishment of the Tsugaru and the Alboran Gyres

A new theory for the generation of the Tsugaru and Alboran gyres is proposed. The essence of the theory can be described as follows. Using the nonlinear reduced-gravity (shallow water) equations, it has been recently shown by Pichevin and Nof that a channel emptying light water into an otherwise resting ocean of denser water on an f plane produces a forever-growing gyre next to the channel mouth. The generation of the gyre is caused by the (otherwise imbalanced) flow force of the alongshore current downstream regardless of the initial current vorticity. [By changing the potential vorticity via friction, the fluid creates the required vorticity (on its own) in the cases where the incoming flow has a vorticity that cannot accommodate the gyre.] It is shown here, analytically and numerically, that when the channel is oriented eastward (i.e., the channel is situated along a western boundary as is the case with the Tsugaru and Alboran gyres) the presence of b causes an arrest of the gyre’s growth. As a result, a steady state corresponding to a flow field resembling a snail is established. Here, the ‘‘shell’’ of the imaginary snail corresponds to the gyre and the elongated body of the snail corresponds to the downstream current. The establishment of the modeled steady gyre is inevitable, regardless of the upstream potential vorticity, and the gyre has a length scale involving both b and the Rossby radius. The analytical solution to the inviscid nonlinear equations is constructed using a perturbation scheme in «, the ratio of the Coriolis parameter variation across the current to the Coriolis parameter at the center. It shows that the gyre size is roughly 2Rd/«1/4 [where Rd is the Rossby radius (based on the downstream thickness H) and «[ bRd/ f 0] implying that the Tsugaru and the Alboran gyres have a scale that is greater than the usual current scale (Rd). Numerical simulations, using the Bleck and Boudra model, are in excellent agreement with the theoretical prediction for the inviscid gyre size; they also show that the gyres are established regardless of the upstream potential vorticity. Both the analytical and the numerical results are in good agreement with the observations.

A Different Outflow Length Scale

Abstract Using a nonlinear “reduced gravity” model it is shown analytically that a large buoyant midlatitude outflow situated along the northern boundary of a β-plane ocean produces an unusually broad westward flow. The steady nonlinear outflow consists of a narrow jet (whose width is the familiar midlatitude Rossby radius) and a broad, nearly stagnant region whose width is the equatorial Rossby radius. The steady, inviscid solution reported here is constructed with the aid of the momentum-flux equation. For high-Rossby-number flows (i.e., zero potential vorticity flows), the total outflows width is ∼1.228 times the equatorial Rossby radius. A finite potential vorticity outflow produces a slightly narrower westward flow. The above solution breaks down in the linear limit, and it is expected that a linear outflow would consist of a single flow whose width is on the order of the midlatitude Rossby radius. Numerical simulations are in very good agreement with the above nonlinear solution. The new southward ...

Eddy Formation and Shedding in a Separating Boundary Current

Abstract This study deals with the separation of western boundary currents within a reduced-gravity framework, and it analyzes the formation of eddies in the separation region and the conditions of their shedding into the open ocean. It shows that the separation point of the current oscillates along the coast so that the retroflected eastward current develops meanders. These meanders grow, drift westward under the influence of β, and finally hit the coastal current, which leads to the periodic formation of eddies. This study also highlights the impact by the geometrical configurations of the flow and coastline upon the existence or lack of a subsequent shedding of these eddies: a shedding occurs when no obstacle hinders the β-induced westward drift of the eddies. This happens when either (i) the current retroflects far enough beyond the tip of the coast so that, because of β, the eddies can propagate westward without being blocked, or (ii) the tilt of the coast is small enough so that the alongshore compo...

Comments on “On the Steadiness of Separating Meandering Currents”

AbstractUsing integration constraints and scale analysis, van Leeuwen and De Ruijter focused on the steady aspect of the downstream flow in the momentum imbalance articles of Nof and Pichevin appearing in the 1990s and later on. They correctly pointed out that when the steady downstream flow is exactly geostrophic then it must obey the additional downstream (critical) condition (where u is the speed, g′ is the reduced gravity, and h is the thickness). They then further argue that this additional condition provides “a strong limitation on the generality of their results.” These results for steady flows have been incorrectly generalized by the typical reader to eddy generating unsteady flows, which was the focus of Nof and Pichevin.The current authors argue that, although the van Leeuwen and De Ruijter condition of is valid for a purely geostrophic and steady flow downstream, it is inapplicable even for the steady aspect of the Nof and Pichevin solutions because the assumption of a purely geostrophic flow (...