Mountain and Lee Waves

Linear Wave Theory - a very brief look

The basic equations to start from are derived from the momentum, continuity, and thermodynamic equations. This eventually gives terms for the steady-state two-dimensional Boussinesq flow.

Where l is the Scorer Parameter.

These are the general equations for the mountain wave sans nonlinear terms. From here, different conditions and assumptions can be set depending on certain parameters.

For U and N set to be constants, one can derive the equations for the sinusoidal mountain range. There is a simplification of boundary conditions that allow for N > 0 and k > 0 without loss of generality.

If one allows U and N to vary with height, then the derivations can be made to derive solutions for an isolated mountain. As opposed to infinitely sinusoidal terms, the ridge takes the form of:

Where a is a unit of distance. The shape of these set the streamlines over the ridge, that assist with the derviations.

One can follow the derivations in (Durran 2003)--or in more detail in book published by AMS--for a full derivation and closer examination of the equations.