Th. doct.-ing.--Paris 7, 1981.

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Thesis (M. Sc.)--York University, 2000. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 59-61). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pMQ67758.

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In the conventional approach to geophysical fluid dynamics, only the horizontal components of the Coriolis force due to horizontal motions of the fluid are taken into account. All the other components of the Coriolis force, which are called the non-traditional (NT) terms, are considered to be small second order quantities and are usually dropped. This effectively simplifies the system and the nice and clean quasi-geostrophic (QG) equation can be obtained, which is widely used in analytical studies of climate systems. Interest has been drawn to the dropped terms in recent studies. It is shown that in some special cases these second order terms actually have a noticeable influence on the dynamics of the system. However, a full picture of these terms in the dynamics of the real ocean is still lacking. Here, we will start from the fundamental equations of fluid dynamics, and through careful scaling analysis conduct a detailed study of the governing equations of geophysical fluid dynamics while keeping the NT terms. We will specifically investigate the influence of these NT terms on equatorial waves, since near the equator the NT components of the Coriolis force are the most significant. / text

The Coriolis force has a subtle, but significant impact on the dynamics of geophysical and astrophysical flows. The Rossby number, Ro, is the nondimensional parameter measuring the relative strength of the Coriolis term to the nonlinear advection terms in the equations of motion. When the rotation is strong, Ro goes to zero and three-dimensional flows are observed to two-dimensionalize. The broad aim of this work is to examine the effect of the strength of rotation on the nonlinear dynamics of turbulent homogeneous flows. Our approach is to decompose the rotating turbulent flow modes into two classes: the zero-frequency 2-dimensional (2D) modes; and the high-frequency inertial waves (3D). / First, using numerical simulations of decaying turbulence over a large range of Ro we identified three regimes. The large Ro regime is similar to non-rotating, isotropic turbulence. The intermediate Ro regime shows strong 3D-to-2D energy transfers and asymmetry between cyclones (corotating) and anticyclones (couter-rotating), whereas at small Ro regime these features are much reduced. / We then studied discreteness effects and constructed a kinematic model to quantify the threshold of nonlinear broadening below which the 2D-3D interactions critical to the intermediate Ro regime are not captured. These results allow for the improvement of numerical studies of rotating turbulence and refine the comparison between results obtained in finite domains and theoretical results derived in unbounded domains. / Using equilibrium statistical mechanics, we examined the hypothesis of decoupling predicted in the small Ro regime. We identified a threshold time, t☆ = 2/Ro2, after which the asymptotic decoupling regime is no longer valid. Beyond t ☆, we show that the quasi-invariants of the decoupled model continue to constrain the system on the short timescales. / We found that the intermediate Ro regime is also present in forced turbulence and that interactions responsible for it are nonlocal. We explain a steep slope obtained in the 2D energy spectrum by a downscale enstrophy transfer. The energy of the 2D modes is observed to accumulate in the largest scales of the domain in the long-time limit. This is reminiscent of the "condensation" observed in classical forced 2D flows and magnetohydrodynamics.

This study intends to recover and expand the analytical work of Vadasz (1998) for linear and weak non-linear stability of a rotating porous media heated form below and subject to gravity and Conolis forces. It is shown that the viscosity has a destabilising effect at high rotation rate. It has been established that the critical wave number in a plane containing the streamlines is dependent on rotation. Finite amplitude calculations provide a set of differential equations for the amplitude and phase, corresponding to the stationary and over-stable convection, identifying the post-transient conditions that a fluid is subject to, i.e. a pitchfork bifurcation for the stationary case, or a Hopf bifurcation in the case of over-stable convection. The previous model (Vadasz [1998]) was extended with an additional time scale in order to represent amplitude fluctuations and a short space scale to include horizontal modes of oscillations. When the complete solution for the stream function or temperature is analysed, where left and right travelling waves are considered, we obtain a set of differential equations for the amplitude and phase. The solutions are discussed in this context. / Thesis (Ph.D.)-University of Durban-Westville, 2000.

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Physical experiments are used to investigate the influence of the Coriolis forces on flow structures in channelized turbidity currents, and their implication for the evolution of straight and sinuous submarine channels. Initial tests were used to determine whether or not saline density currents are a good surrogate for particle-laden currents. Results imply that this assumption is valid when turbidity currents are weakly-depositional and have similar velocity and turbulence structures to saline density currents. Second, the controls of Coriolis forces on flow structures in straight channel sections are compared with two mathematical models: Ekman boundary layer dynamics and the theory of Komar [1969]. Ekman boundary layer dynamics prove to be a more suitable description of flow structures in rotating turbidity currents and should be used to derive flow parameters from submarine channels systems that are subjected to Coriolis forces. The significance of Coriolis forces for submarine channel systems were determined by evaluating the dimensionless Rossby number RoW. The Rossby number is defined as the ratio of the flow velocity, U, of a turbidity current to the channel width, W, and the rotation rate of the Earth represented by the Coriolis parameter, f. Coriolis forces are very significant for channel systems with RoW ≤ O(1). Third, the effect of Coriolis forces on the internal flow structure in sinuous submarine channels is considered. Since previous studies have only considered pressure gradient and centrifugal forces, the Coriolis force provides a crucial contribution to the lateral momentum balance in channel bends. In a curved channel, both the Rossby number RoW and the ratio of the channel curvature radius R to the channel width W, determine whether Coriolis forces affect the internal flow structure. The results demonstrate that Coriolis forces can cause a significant shift of the density interface and the downstream velocity core of channelized turbidity currents. The sediment transport regime in high-latitude channel systems, which have RoW << R/W, is therefore strongly influenced by Coriolis forces. Finally, these findings are incorporated into a conceptual model describing the evolution of submarine channels at different latitudes. For instance, the Northern Hemisphere channels have a distinctly higher right levee system and migrate predominantly to the left side and generally exhibit a low sinuosity. In contrast, low latitude channel systems have RoW >> R/W so that centrifugal forces are more dominant. This results in more sinuous submarine channel systems with varying levee asymmetries in subsequent channel bends. In conclusion, Coriolis forces are negligible around the equator but should be considered in high latitude systems, particularly when RoW ~ O(1) and RoW << R/W.