where c is the celerity (speed) of long gravity waves in the water body of interest, where we define long waves as those whose wavelength is far greater than the water depth. For surface ('barotropic') waves c = y/gH, where g is the gravitational constant (9.8 ms-2) and H is the water depth, as described in the preceding article.

Note that it is possible to represent a stratified system as an equivalent depth of homogenous fluid so that the internal ('baroclinic') dynamics can be represented by the same equations. For example, for a two-layer stratification, we can define the equivalent depth as

where p is the density and h the depth and the subscripts refer to the upper and lower layer. This allows for simple definition of the barotropic phase speed as c = yjgp, and the baroclinic phase speed as ci = VgHe, and also allows us to define an internal Rossby radius of deformation that applies to barocli-nic processes (those due to stratification) as

The equivalent depth can also be defined for a continuous stratification, using cm in eqn. [17] discussed later in this chapter.

We also define the Burger number

where L is a length characterizing the basin length and/or width and R can represent either the Rossby radius or the internal Rossby radius. This dimension-less number is used to help classify both vorticity and gravity waves, and has been called by various names in the literature, such as the stratification parameter or nondimensional channel width. It is simply the ratio of the length scales at which rotation effects become important to the length scale of the lake in question, so for S ! 0 rotation is very important for c

the dynamics, and for S rotation can be ignored as the lake is physically small. Note that there is no abrupt transition, where the effects of rotation are suddenly felt at S = 1, but a gradual transition - this will be discussed later in this article.

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