The problem of a recirculation gyre driven by a zonal jet on a β plane is considered. In a limiting case of a strong jet, when the structure of the flow depends only on the momentum flux J of the jet, an asymptotic scaling law for the recirculation gyre is derived: the meridional extent of the gyre depends only on the balance between the inertia of the jet and the opposing β effect, YG = (540J/β2)1/5, while the zonal extent XG is linearly proportional to the Reynolds number, Re. Analysis of steady numerical solutions confirms the scaling law. A simplified model of the flow as a combination of a jet carrying a positive momentum flux and a homogenized core of the recirculation gyre carrying an opposite amount of momentum flux provides the quantitative constant in the scaling law, which is in good agreement with the numerical results. Also the gyre is found to form only when the flow in the channel is supercritical with respect to Rossby waves. Thus the recirculation on the β plane can be regarded as a feature similar to a submerged hydraulic jump: a transition between the supercritical flow within the channel and the subcritical (vanishing) flow in the Sverdrup interior of the basin. Laboratory experiments validate the numerical model: there is quantitative agreement with steady solutions and tracer evolution for low Re when flow is close to laminar; for higher Re laboratory experiments show richer behavior, with a strong tendency to asymmetric solutions. Application of the results to the Gulf Stream system is discussed: the meridional scale of the Gulf Stream recirculation YG = 470 km or 4.2° latitude is predicted, which is consistent with observational data.
Corresponding author address: Dr. Vitalii A. Sheremet, Woods Hole Oceanographic Institution, MS #21, Woods Hole, MA 02543. Email: email@example.com