Equatorial waves

The Yanai wave is a term from the wave theory.

Description

Yanai waves are movements in the oceans and in the atmosphere, which in-situ measurements and with the help of satellites are made observable. They play a crucial role for tropical instabilities and for the climate phenomenon El Niño.

Yanai waves follow the motion equations of hydrodynamics. To arrive at certain wave solutions for this system of equations, one needs to adapt this hydrodynamic system of equations of the problem under consideration, that is, that you may certain approximations ( for example, the Boussinesq approximation ) or transformations makes for easier on the desired solution come.

A special case that can be considered in this system of equations and for an adjustment is required, the equatorial dynamics. A parameter that is in the equations, namely the Coriolis parameter, which is zero at the equator. This means for the equations that is obtained there a singularity can be circumvented with the mathematically difficult. Therefore, it results in this special case, a so-called β - level, which allows a wide variation of the dependent Coriolisparameters a reference width, and thus circumvents the problem. So to now to study the Yanaiwellen come, so placing the equatorial β -plane equations based.

The following applies:

Now, to get to the dispersion relation, which indicates the relationship between the frequency and the wave number and the examination can give us information about the behavior of Yanai waves, you go with an exponential approach of the form

In the inside system of equations. It showed w is the frequency dar. That is one continues this approach, a simple and gets the dispersion relation

The mode number m is a natural number.

This one captures different types of equatorial waves.

The special dispersion relation of the Yanai wave is obtained for the case m = 0

Evaluation of the dispersion relation

In the same form can be considered dispersion relations for different wave types with other approximations. It then provides the connection between frequency and wave number for different wave types is, we obtain the following graph:

It is clear, therefore, that the Yanai wave behaves at low frequencies as a Rossbywelle with westwärtiger phase velocity and high frequencies as a gravity wave with phase velocity ostwärtiger. Because of this mixed behavior, the Yanai wave is also mixed Rossby - gravity wave (engl: mixed Rossby -gravity wave) called. The group velocity is directed to Yanai waves always the east and lies in the order of 2 to 3 m / s This means that these waves can move relatively quickly eastward over the equatorial ocean and that, for example, about need a month to cross the Pacific Ocean at the Equator.