By Derome J., Zhang D.L.

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In case (ii), we have ω2 dvˆ 2 2[k ] vˆ = 0, c02 dy 2 which yields the solution of high-frequency gravity waves or Poincaré waves, provided ω = ± c02 (k2 + n2) . Therefore, the complexity with Eq. (4) comes from the fact that the coefficient in square brackets is not a constant but a function of y. Eq. (4) is actually a form of the Schrödinger equation for a simple harmonic oscillator in y, and it has solutions of the form exp (± y2/2). Only the decaying solutions, however, can satisfy the boundary conditions.

The results are shown in Fig. 11. The vertical levels are indicated roughly as a function of p/p0 and the modes are ordered by decreasing equivalent depth. In this case, the barotropic mode has an equivalent depth of 9570 m, while the smallest equivalent depth is only 3 m. (1c)]. On the other hand, if the divergence effect is large, the wave mode must have small equivalent depth. Similarly, we may obtain a vertical structure equation for equatorial waves (not shown herein). However, if frequency and wavenumbers are known from observations, the equivalent depth for equatorial waves can be directly obtained from Eq.

Another important feature of Kelvin waves is that there is no flow component normal to the coastal line. Similar characteristics of Kelvin waves have also been found in the lower portion of the stratosphere in the tropics. Observations indicate that tropical Kelvin waves, having a period of 15 days and wavelength of 20,000-40,000 km, propagate eastward at a speed around 25 m s-1. In the tropics, there are no "physical coastal 44 boundaries" but owing to the change in the sign of the Coriolis parameter, the equator acts like "a boundary" in the generation of the observed Kelvin wave structures.