The establishment of the Tsugaru and the Alboran gyres

Abstract

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 β causes an arrest of the gyre's growth. As a result, a steady state corresponding to a flow 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 β and the Rossby radius. The analytical solution to the inviscid nonlinear equations is constructed using a perturbation scheme in ε, 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 2R(d)ζε( 1/4 ) [where R(d) is the Rossby radius (based on the downstream thickeness H) and ε ≡ βR(d)ζf0] implying that the Tsugaru and the Alboran gyres have a scale that is greater than the usual current scale (R(d)). 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.