Where the \ phi _ x are geopotential height fields with \ phi _ 1 > \ phi _ 0, f is the Coriolis parameter, and \ mathbf { k } is the upward-pointing unit vector in the vertical direction.
22.
Where h is the upper-layer thickness anomaly, ? is the wind stress, c is the Rossby wave speed that depends on latitude, ? 0 is the density of sea water and f 0 is the Coriolis parameter at a reference latitude.
23.
The solutions of ( 5 ) with boundary condition that \ psi be constant on the coastlines, and for different values of \ alpha, emphasize the role of the variation of the Coriolis parameter with latitude in inciting the strengthening of western boundary currents.
24.
Where \ u and \ v are the velocities in the \ x and \ y directions, respectively, \ f is the local Coriolis parameter, and \ K _ m is the diffusive eddy viscosity, which can be derived using mixing length theory.
25.
In particular, Rossby waves, the most important type of waves if one considers large-scale atmospheric and oceanic dynamics, depend on the variation of " f " as a restoring force; they do not occur if the Coriolis parameter is approximated only as a constant.
26.
Where f is the Coriolis parameter, \ sigma is related to the geostrophic velocity vector, \ zeta _ g is the geostrophic relative vorticity, \ phi is the geopotential, \ nabla ^ 2 _ H is the horizontal Laplacian operator and \ nabla _ H is the horizontal del operator.
27.
The adjustment process tends to take place in two distinct stages where the first stage is a rapid change due to the fast propagation of gravity waves, the same as that on an " f "-plane ( Coriolis parameter held constant ), resulting in a flow that is close to geostrophic equilibrium.
28.
In 1948, Henry Stommel published a paper in " Transactions, American Geophysical Union " titled " The Westward Intensification of Wind-Driven Ocean Currents ", in which he used a simple, homogeneous, rectangular ocean model to examine the streamlines and surface height contours for an ocean at a non-rotating frame, an ocean characterized by a constant Coriolis parameter and finally, a real-case ocean basin with a latitudinally-varying Coriolis parameter.
29.
In 1948, Henry Stommel published a paper in " Transactions, American Geophysical Union " titled " The Westward Intensification of Wind-Driven Ocean Currents ", in which he used a simple, homogeneous, rectangular ocean model to examine the streamlines and surface height contours for an ocean at a non-rotating frame, an ocean characterized by a constant Coriolis parameter and finally, a real-case ocean basin with a latitudinally-varying Coriolis parameter.
30.
Further \ rho is the fluid density, \ times is the cross product operator, \ boldsymbol { f } = f \ hat { \ boldsymbol { z } } where f = 2 \ Omega \ sin \ phi is the Coriolis parameter ( with \ Omega the Earth's rotation angular speed and \ sin \ phi the sine of the latitude ) and \ hat { \ boldsymbol { z } } is the unit vector in the vertical upward direction ( opposing the Earth's gravity ).
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