The quasi-geostrophic fluid is an important model in geophysical fluid dynamics, they are special cases of the general quasi-geostrophic approximations for atmospheric and oceanic fluid flow with the small local Rossby number
which ensures the validity of the geostrophic balance between the pressure gradient and the Coriolis force.
In these model experiments various combinations of Rossby number (Ro=U/fL) and Reynolds number (Re=UL/v) were tried (here U is the inflow velocity, f is the rotation rate, L is the horizontal scale of the basin, and vis the molecular viscosity).
The authors concluded that the westward penetration of the LC intensifies as the Rossby number and Ekman number (Ek=v/f[L.sup.2]) decrease.
Their results show that the northward penetration length of the loop is proportional to a parameter called penetration Rossby number (Rp=[(2QLe/[ohm][alpha]).sup.1/4]/L where Q is the inflow volume transport, Le is the equivalent length of the approaching channel, [ohm] is the angular velocity of the table, [alpha] is the bottom slope, and L is the distance between the inlet and the outlet.
Thus, the flow is controlled by the following non-dimensional parameters: the Rossby number Ro = U/fL = g'H/[f.sup.2][L.sup.2], which is the ratio of the inertial force to the Coriolis force; the Ekman number Ek = [v.sub.1]/f[L.sup.2] = [v.sub.z]/f[H.sup.2], which is the ratio of the viscous force to the Coriolis force; and the Prandtl number Pr = v/[kappa], which is the ratio of the viscosity to the diffusivity, where v is a coefficient of kinematic viscosity and [kappa] is a coefficient of diffusivity.
The external forcing parameter (q), as well as the Rossby number (Ro), had values of the order of [10.sup.-3], and the horizontal Ekman number (Ek) was of the order of [10.sup.-6] for both the model and the Gulf.
In laboratory tests, the Rossby number was set between 1x[l0.sup.-4] <Ro<2000x[10.sup.-4], and the horizontal Ekman number varied between 0 * 3x[10.sup.-6] <Ek<130x[l0.sup.-6].