By Derome J., Zhang D.L.

**Read or Download A short course on atmospheric and oceanic waves PDF**

**Similar physics books**

**Vibrations of Shells and Plates, Third Edition **

With more and more subtle constructions considering sleek engineering, wisdom of the complicated vibration habit of plates, shells, curved membranes, jewelry, and different complicated constructions is vital for today’s engineering scholars, because the habit is essentially diverse than that of easy buildings equivalent to rods and beams.

- Forced vibrations of a nonhomogeneous string
- Numerical Shape Optimization in Structural Acoustics
- Amateur Telescope Making (1998)(en)(259s)
- Statistische Mechanik
- Astrophysics in the Next Decade: The James Webb Space Telescope and Concurrent Facilities

**Additional resources for A short course on atmospheric and oceanic waves**

**Example text**

26 3. 1 Rossby waves In the preceding section, we obtained for surface inertial-gravity waves a cut-off frequency of ω = f at which both the earth's rotation and gravity are important. Does this imply that there would be no waves falling into the frequency range ω < f? The answer is: yes or no. Recall that in our previous model, the Coriolis parameter, f, was treated as a constant, namely, the earth curvature has been neglected. This assumption is valid only when the application range of latitude is small.

If we define β = ∂f/∂y (or β plane approximation)2 as the rate of change of f with latitude, and introduce the perturbation stream function based on Eq. (1c): u' = - ∂ψ , ∂y v' = ∂ψ , ∂x and ζ' = Δψ, then Eq. (2) becomes ( 2 ∂ ∂ ∂ψ + U ) Δψ + β = 0. 6 x 10-11 m1 s-1 at φ = 450, where a is the radius of the earth. The β-plane approximation is generally adequate when the wavelength of a Rossby wave is smaller than the earth's radius. 28 Substituting the following form of wave solution ψ = A e i(kx + ly - ωt) into (3) yields the frequency equation (ω - kU) (k2 + 2) + βk = 0, β ω = k(U - 2 ), (4) K where K2 = k2 + 2.

8a) implies that for a basic state in geostrophic balance, the free surface must slope to provide a pressure gradient force to balance the Coriolis force. Thus, the linearized continuity equation becomes ( or ∂H ∂ ∂ ∂u ' ∂v' + U )h' + v' + H( + ) = 0, ∂y ∂y ∂t ∂x ∂x ∂h' ∂u ' ∂v' + H( + ) = 0. ∂y ∂t ∂x (9) (9') Note that the geostrophic relation has been used to cancel U∂h'/∂x and v'∂H/∂y. We will treat H as constant except when taking derivatives, since the height difference caused by the sloping surface is very small, as compared to the depth of the fluid.