Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 161-165).

Thesis--Wisconsin. / Includes bibliographical references (leaves 30-31).

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The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance for the circulation of the atmosphere and oceans, mainly because of the momentum and energy they transport and because of the mixing they create upon breaking. So far the study of inertia-gravity waves has answered a number of questions about their propagation and dissipation, but many aspects of their generation remain poorly understood. The interactions that take place between the slow motion, termed balanced or vortical motion, and the fast inertia-gravity wave modes provide mechanisms for inertia-gravity wave generation. One of these is the instability of balanced flows to gravity-wave-like perturbations; another is the so-called spontaneous generation in which a slowly evolving solution has a small gravity-wave component intrinsically coupled to it. In this thesis, we derive and study a simple model of inertia-gravity wave generation which considers the evolution of a small-scale, small amplitude perturbation superimposed on a large-scale, possibly time-dependent °ow. The assumed spatial-scale separation makes it possible to apply a WKB approach which models the perturbation to the flow as a wavepacket. The evolution of this wavepacket is governed by a set of ordinary differential equations for its position, wavevector and its three amplitudes. In the case of a uniform flow (and only in this case) the three amplitudes can be identifed with the amplitudes of the vortical mode and the two inertia-gravity wave modes. The approach makes no assumption on the Rossby number, which measures the time-scale separation between the balanced motion and the inertia-gravity waves. The model that we derive is first used to examine simple time-independent flows, then flows that are generated by point vortices, including a point-vortex dipole and more complicated flows generated by several point vortices. Particular attention is also paid to a flow with uniform vorticity and elliptical streamlines which is the standard model of elliptic instability. In this case, the amplitude of the perturbation obeys a Hill equation. We solve the corresponding Floquet problem asymptotically in the limit of small Rossby number and conclude that the inertia-gravity wave perturbation grows with a growth rate that is exponentially small in the Rossby number. Finally, we apply the WKB approach to a flow obtained in a baroclinic lifecycle simulation. The analysis highlights the importance of the Lagrangian time dependence for inertia-gravity wave generation: rapid changes in the strain field experienced along wavepacket trajectories (which coincide with fluid-particle trajectories in our model) are shown to lead to substantial wave generation.

ABSTRACT This paper treats the standing waves formed by two progressive waves possessing same properties but opposite direction in stationary atmosphere and uniform depth. The third-order approximation to two-wave trains interactions obtained by Chen¡]1990¡^is cited. From the solution that can be reduced to the cases such as standing waves, the properties resulted in standing wave due to the nonlinear interactions between two wave trains intersection, particularly, the two peaks of wave pressure, are described clearly. Furthermore, the profile, pressure and angular frequency is also verified in good agreement with the experimental results.

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The linear and weakly non-linear limits of two-dimensional gravity waves in an incompressible, inviscid and stably stratified atmosphere are studied. The linear results indicate the growth of waves propagating upward leading to the breakdown of the linear theory. The three-wave resonant interaction theory indicates an energy cascade from a vertically propagating wave (primary wave) to waves having smaller absolute values of Doppler shifted frequency ((OMEGA)). When the non-dimensional parameter / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / is in the range "1 to about 0.8" (N being the Brunt-Vaisala frequency), the energy of the primary wave is transferred to bands of small amplitude waves. The triads in these bands include a member with the same vertical group velocity as the primary wave while other triads contain a member with larger vertical group velocity. The band widths approach zero as the primary wave amplitude is reduced. The analysis suggests that the three-wave resonant interactions should be replaced by a higher order approximation in this limit.

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Copy of author's previously published article inserted. / Bibliography: p. 239-253. / xxx, 253, [42] p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis is concerned with the determination of gravity wave characteristics using operational radiosondes. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1996?