Second order Rossby-Haurwitz wave interactions

Rossby-Haurwitz waves are large sinuous oscillations in the atmosphere and oceans. These planetary waves owe their existence to the rotation and shape of the earth. They are an important wave type for large-scale meteorological processes as they are dominant in determining the patterns of weather in the middle latitudes.\ud \ud This thesis concerns the interactions of these Rossby-Haurwitz waves within the framework of the vorticity equation for nondivergent planetary flow at second order. O f particular interest is the potential for generating zonal flow, i.e., large-scale atmospheric flow th at occurs in an east-west direction. Examining interactions at first order we distinguish between nonresonant interactions and resonant interactions. Resonant interactions are interactions where two Rossby-Haurwitz waves can create a th ird Rossby-Haurwitz wave, which over time becomes as strong as the two primary waves. The necessary conditions for resonant interactions to occur are derived. I t is also shown th at zonal flow waves cannot be produced at this order.\ud \ud Examining second order interactions it is shown that zonal flow can now be generated by a mechanism that disappears in the ¡3—plane limit. This is the central result of the thesis. Zonal flow can be generated through the exchange of energy within a triad, and this occurs at second order. The amplitudes of the zonal flow terms are not affected until the second order equation. Detailed numerical results are presented underpinning the theoretical results