Article Contents
Article Contents

# The surface current of Ekman flows with time-dependent eddy viscosity

• In this paper we investigate transients in the oceanic Ekman layer in the presence of time-varying winds and a constant-in-depth but time dependent eddy viscosity, where the initial state is taken to be the steady state corresponding to the initial wind and the initial eddy viscosity. For this specific situation, a formula for the evolution of the surface current can be derived explicitly. We show that, if the wind and the eddy viscosity converge toward constant values for large times, under mild assumptions on their convergence rate the solution converges toward the corresponding steady state. The time evolution of the surface current and the surface deflection angle is visualized with the aid of simple numerical plots for some specific examples.

Mathematics Subject Classification: 35G16, 76U60, 86A05.

 Citation:

• Figure 1.  Plots of $\tan(\theta_0(t))$ (left) and the (normalized) velocity components (right) for $K(t) = c\vert\tau(t)\vert$ and $\tau(t) = 2- \mathrm{e}^{-t^2}$

Figure 2.  Plots of $\tan(\theta_0(t))$ (left) and the (normalized) velocity components (right) for $\tau(t) = 1+ \mathrm{e}^{-t^2}$

Figure 3.  Plots of $\tan(\theta_0(t))$ (left) and the (normalized) velocity components (right) for $\tau(t) = 1+2t^2\left(1-\frac{3}{4}t^2\right) \mathrm{e}^{-t^2}$

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