By Derome J., Zhang D.L.
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Additional info for A short course on atmospheric and oceanic waves
2 − kω gH − β gH = 0, or ω2 (gH)1/2 = β+kω . (12) With typical values for ω, β, and k, the equivalent depth for mixed Rossby-gravity waves is less than 100 m. Clearly, it is the smallness of equivalent depth that makes it difficult to separate the Rossby mode from the gravity mode in the tropics. 2). It is evident that the magnitude of equivalent depth determines the relative significance of divergence in the wave propagation in the atmosphere or other stratified fluids. For a more detailed discussion of the equivalent depth, the reader is referred to the review paper by Daley (1981, Rev.
There are also vertically propagating Rossby-gravity waves and Kelvin waves in a stratified flow, which will not be discussed in this course. See the original paper by Matsuno (1966: JMSJ) for more detailed discussions. , k = 4) and a period of 4 - 5 days. It has also been referred to as Yanai waves. For simplicity, we consider the linearized momentum and continuity equations for a fluid with an equivalent depth H in a motionless basic state, so we may use the same set of equations as that for the discussion of divergent Rossby waves.
5) In contrast to gravity waves, which can propagate in two opposite directions, Rossby waves always have easterly phase speed relative to the mean flow. This one-directional propagation property is apparently due to the fact that the earth has a preferred direction of rotation. Note though that as K2 gets larger, Rossby waves move more and more closer to the mean flow and become stationary at K2 = β/U. t. the earth, and longer waves (k2<β/U) move westward in the presence of a mean flow. 5 m s-1.
A short course on atmospheric and oceanic waves by Derome J., Zhang D.L.