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 time) quickly at the rate of 8g?Q/3πf2R3 (where g? is the reduced gravity, Q is the outflow's discharge, f the Coriolis parameter, and R is the instantaneous bulge radius). Such an intense (large Rossby number) outflow dumps most of its mass flux (66%) into the growing bulge rather than into the longshore current downstream (which receives the remaining 33% of the total flux). An outflow with a weakly anticyclonic vorticity (?αf, where α is analogous to the Rossby number and is much smaller than unity), on the other hand, dumps most of its water [(1 ? 2α)Q] into the downstream current rather than into the bulge. Even though less mass flux is going into the bulge in this weak vorticity case, the bulge balloons at a somewhat faster rate (4g?Q/πf2R3) than the intense outflow does because the bulge is now relatively flat so that most of the incoming water goes toward an increase in size rather than toward an increase in thickness. Numerical simulations are in good agreement with the above analytical solutions. They show that frictional forces increase the downstream current mass flux. The simulations also show that friction very gradually alters the potential vorticity of the bulge. Applications to the initial growing stage of Loop Current rings (which constitute an ?outflow bulge? in the sense that it corresponds to water flowing from the Caribbean into the Gulf of Mexico), to rivers outflow, to bulges of plumes in other numerical models, and to bulges in laboratory outflows are discussed.