Barotropic Currents Research Articles

On stationary topography-induced rossby-wave patterns in a barotropic zonal current

The present remarks concern the modification, by a bottom-topographical feature or other stationary perturbing effect, of a uniform zonal frictionless barotropic current in a betaplane. Simple examples illustrate the fact that there are several qualitatively distinct ways in which the zonal current can be affected by the topography.

順圧不安定に対する差分近似

The validitiy of finite difference approximations in solving the dynamic instability problem of non-divergent barotropic currents is examined numerically.We first study the instability of a sine-curve symmetric zonal current confined between two rigid walls. The relation between the solutions of the finite difference equations and those of the original differential equation is discussed. Then the accuracy of the finite difference method in describing the instability is examined by varying the number of subdivisions. For a sufficiently accurate description of the instability, a large number of subdivisions, at least 20, are required for this velocity profile.We then study the instability of a symmetric and an antisymmertic zonal currents extending to infinity. The effect of rigid boundaries placed at a finite distance from the central shearing wind belt on the critical wavelengths is examined by varying the position of the boundaries. For both velocity profiles, it is shown that the exact boundary conditions at infinity can be replaced by rigid boundary conditions at a distance equal to the half width of the shearing wind belt.

The Influence of Viscous Boundary Layers on Transient Motions in a Stratified Rotating Fluid. Part II.

Abstract The response of an unbounded ocean to circularly symmetric time varying wind stresses is analyzed. A continuously stratified ocean is first considered. The model includes bottom friction, but the Coriolis parameter is a constant. It is shown that in a stratified ocean both barotropic and baroclinic currents are generated by wind stresses. The barotropic current, however, has its amplitude limited by bottom friction, so that the baroclinic mode dominates for long period forcing. A simple analytic approximation to the depth dependence of static stability in the oceans is introduced and shown to give more realistic results than a constant static stability model. A two-layer model including both a variable Coriolis parameter and bottom friction is analysed. This simple model indicates that both bottom friction and the variation of the Coriolis force enhance the baroclinic mode.

The barotropic stability of the mean winds in the atmosphere

This paper considers the stability of a barotropic current on a beta earth. The motion is assumed to be horizontal, non-divergent and barotropic. The current is taken to be of the formU(y)=Asech2by+B. The perturbations are required to approach zero asyapproaches ± ∞. We introduce the non-dimensional wave-numberland a parameter χ, which is a measure of the rotation effect. χ is inversely proportional to β.There are only two kinds of perturbations: symmetric disturbances (those with maximum amplitude aty= 0) and antisymmetric disturbances (those with zero amplitude aty= 0). We find the neutral curve in the (χ,l2)-plane for both types of disturbances. The rates of amplification in the immediate vicinity of the neutral curves are also found. It is seen that the beta effect, which is due to the earth's rotation, tends to stabilize the current. For the symmetric disturbances we find a band of unstable wavelengths when χ > 1/2; and for large χ the estimated curve of the maximum value of the imaginary part of the phase velocity is asymptotic to the lower branch of the neutral curve. The antisymmetric disturbances are more stable than the symmetric disturbances.