P

nn inny\ Tn v = fx =--r— sin -n [1 - H (L + cnt - x)] (4.516)

Fig. 4.94 Analytical barotropic wave solution for the first few time steps (time in nondimensional units, a t = 5, b t = 10, c t = 15). The heavy solid lines for the Rossby waves reflected from the western boundary, and the thin solid line for the sum of the transient part and the stationary part, as defined in Eqn. (4.511).

Fig. 4.94 Analytical barotropic wave solution for the first few time steps (time in nondimensional units, a t = 5, b t = 10, c t = 15). The heavy solid lines for the Rossby waves reflected from the western boundary, and the thin solid line for the sum of the transient part and the stationary part, as defined in Eqn. (4.511).

where H(x) is the Heaviside function (or the step function): H(x < 0) = 0, H(x > 0) = 1. This phenomenon can be seen in Figure 4.94.

At any given station x, the Sverdrup flow is established by time (x — L) /cn. Until this time, i.e., if L + cnt — x > 0, the flow is still evolving with

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