Wave radiation is an important process in many geophysical flows. In particular, it is by wave radiation that flows may adjust to a state for which the dynamics is slow. Such a state is described as “balanced”, meaning there is an approximate balance between the Coriolis force and horizontal pressure gradients, and between buoyancy and vertical pressure gradients. In this thesis, wave radiation processes relevant to these enormously complex flows are studied through the use of some highly simplified models, and a parallel aim is to develop accurate numerical techniques for doing so. This thesis is divided into three main parts. 1. We consider accurate numerical boundary conditions for various equations which support wave radiation to infinity. Particular attention is given to discretely non-reflecting boundary conditions, which are derived directly from a discretised scheme. Such a boundary condition is studied in the case of the 1-d Klein-Gordon equation. The limitations concerning the practical implementation of this scheme are explored and some possible improvements are suggested. A stability analysis is developed which yields a simple stability criterion that is useful when tuning the boundary condition. The practical use of higher-order boundary conditions for the 2-d shallow water equations is also explored; the accuracy of such a method is assessed when combined with a particular interior scheme, and an analysis based on matrix pseudospectra reveals something of the stability of such a method. 2. Large-scale atmospheric and oceanic flows are examples of systems with a wide timescale separation, determined by a small parameter. In addition they both undergo constant random forcing. The five component Lorenz-Krishnamurthy system is a system with a timescale separation controlled by a small parameter, and we employ it as a model of the forced ocean by further adding a random forcing of the slow variables, and introduce wave radiation to infinity by the addition of a dispersive PDE. The dynamics are reduced by deriving balance relations, and numerical experiments are used to assess the effects of energy radiation by fast waves. 3. We study quasimodes, which demonstrate the existence of associated Landau poles of a system. In this thesis, we consider a simple model of wave radiation that exhibits quasimodes, that allows us to derive some explicit analytical results, as opposed to physically realistic geophysical fluid systems for which such results are often unavailable, necessitating recourse to numerical techniques. The growth rates obtained for this system, which is an extension of one considered by Lamb, are confirmed using numerical experiments.

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

In this thesis a number of issues related to oceanographic problems have been dealt with on the basis of applying asymptotic methods.  The first study focused on the tidal generation of internal waves, a process which is quantifed by the conversion rates. These have traditionally been calculated by using the WKB approximation. However, the systematic imprecision of this theory for the lowest modes as well as turbulence at the seabed level affect the results. To handle these anomalies we introduced another asymptotic technique, homogenization theory, which led to signifcant improvements, especially for the lowest modes.  The second study dealt with the dynamical aspects of a nonlinear oscillator which can be interpreted as a variant of the classical two-box models used in oceanography. The system is constituted by two connected vessels containing a fluid characterised by a nonlinear equation of state and a large volume differences between the vessels is prescribed. It is recognised that the system, when performing relaxation oscillations, exhibits almost-discontinuous jumps between the two branches of the slow manifold of the problem. The lowest-order analysis yielded reasonable correspondence with the numerical results.  The third study is an extension of the lowest-order approximation of the relaxation oscillations undertaken in the previous paper. A Mandelstam condition is imposed on the system by assuming that the total heat content of the system is conserved during the discontinuous jumps.  In the fourth study an asymptotic analysis is carried out to examine the oscillatory behaviour of the thermal oscillator. It is found that the analytically determined corrections to the zeroth-order analysis yield overall satisfying results even for comparatively large values of the vessel-volume ratio. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.

The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

In this thesis, we study the effect of diurnally- and seasonally-varying forcing on the global circulation of planetary atmospheres explored within a large parameter space. This work focusses on studying the spacial and spectral energy budgets across a large range of planetary parameters as well as the momentum transfer as a response to diurnal and seasonal effects. We simulate planetary atmospheres using PUMA-GT, a simple GCM co-developed for this work, that is forced by a semi-grey two-band radiative-convective scheme, dissipated by Rayleigh friction and allows for temporally varying insolation. Our parameter regime includes the variation of the planetary rotation rate, frictional timescale in the boundary layer, the thermal inertia of the surface and the atmosphere, as well as the short-wave optical thickness. We calculate the energy transfer in Martian atmosphere to have a reference case of an atmosphere that is subject to very strong seasonal and diurnal variation. For this we present the first Lorenz energy budget calculated from reanalysis data of a non-Earth planet. A comparison between Martian and Earth atmosphere reveals a fundamentally different behaviour of the barotropic conversion term in the global mean. A significant impact of the thermal tide can be discerned in the generation of eddy kinetic energy, especially during global dust storms. Our study of seasonal variation reaffirms previous work that the equatorial super-rotating jet in the slow-rotating regime is arrested for strong seasonal variation. We find a novel explanation as to why the Titan atmosphere is able to maintain super-rotation despite strong surface seasonality; for non-zero short-wave absorption in the atmosphere the mechanism that hinders equatorial super-rotation is weakened. Diurnally-varying forcing can significantly enhance the equatorial super-rotation in cases with non-zero short-wave absorption. In our simulations this enhancement is maintained by a convergence of vertical momentum flux at the equator. Efforts to identify the atmospheric waves involved in this enhancement point towards thermally-excited gravity waves.

<div> <div> <div> <p>The combination of field-based studies and numerical modeling provides a robust tool for evaluating geologic and geodynamic processes along a convergent margin. Complex and persistent tectonic activity and a novel suite of geophysical observations make the southern Alaskan convergent margin a key region to evaluate these processes through both basin analysis studies and geodynamic modeling. This conceptual approach is utilized to explore the active driving forces of surface deformation throughout southcentral Alaska, as well as the geologic record of regional Cenozoic tectonic processes. </p> <p>New sedimentologic, chronostratigraphic, and provenance data from strata that crop out within the central Alaska Range document a previously unrecognized stage of Eocene – early Miocene strike-slip basin development along the northern side of the central Denali fault system. This stage was followed by Miocene-Pliocene deformation and exhumation of the central Alaska Range, and basin development and northward sediment transport into the Tanana foreland basin. This portion of the study provides insight into Cenozoic tectonics and basin development in the central Alaska Range. </p> <p>How transpressional tectonics are manifest in the modern-day, in combination with shallow subduction processes, are not well understood for the southern Alaskan convergent margin. Simulations of the 3-D deformation of this region allow for investigation of the complex relationship between these tectonic processes and surface deformation. Results from this study display the far-field affect that strong plate coupling along the shallowly subducting Yakutat slab has on the surface deformation of southcentral Alaska. Our models also show that partitioning of this convergence is observed along the Denali fault system. Additionally, our results indicate the subducting slab is segmented into separate Pacific, Yakutat and Wrangell slab segments. This variation in slab structure exerts control on the upper plate response to shallow subduction.</p> </div> </div> </div>

Waves, which arise when restoring forces act on small perturbations, are ubiquitous in fluids. Their counterpart, mean flows, capture the remainder of the motion and are often characterised by a slower evolution and larger scale patterns. Waves and mean flows, which are typically separated by time- or space-averaging, interact, and this interaction is central to many fluid-dynamical phenomena. Wave-mean flow interactions can be classified into dissipative interactions and non-dissipative interactions. The former is important for small-scale flows, the latter for large-scale flows. In this thesis these two kinds of interactions are studied in the context of microfluidics and geophysical applications. Viscous wave-mean flow interactions are studied in two microfluidic problems. Both are motivated by the rapidly increasing number of microfluidic devices that rely on the mean-flow generated by dissipating acoustic waves - acoustic streaming - to drive small-scale flows. The first problem concerns the effect of boundary slip on steady acoustic streaming, which we argue is important because of the high frequencies employed. By applying matched asympototics, we obtain the form of the mean flow as a function of a new non-dimensional parameter measuring the importance of the boundary slip. The second problem examined is the development of a theory applicable to experiments and devices in which rigid particles are manipulated or used as passive tracers in an acoustic wave field. Previous work obtained dynamical equations governing the mean motion of such particles in a largely heuristic way. To obtain a reliable mean dynamical equation for particles, we apply a systematic multiscale approach that captures a broad range of parameter space. Our results clarify the limits of validity of previous work and identify a new parameter regime where the motion of particles and of the surrounding fluid are coupled nonlinearly. Non-dissipative wave-mean flow interactions are studied in two geophysical fluid problems. (i) Motivated by the open question of mesoscale energy transfer in the ocean, we study the interaction between a mesoscale mean flow and near-inertial waves. By applying generalized Lagrangian mean theory, Whitham averaging and variational calculus, we obtain a Hamiltonian wave-mean flow model which combines the familiar quasi-geostrophic model with the Young & Ben Jelloul model of near-inertial waves. This research unveils a new mechanism of mesoscale energy dissipation: near-inertial waves extract energy from the mesoscale ow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. (ii) We study the interaction between topographic waves and an unidirectional mean flow at an inertial level, that is, at the altitude where the Doppler-shifted frequency of the waves match the Coriolis parameter. This interaction can be described using linear theory, using a combination of WKB and saddle-point methods, leading to explicit expressions for the mean-flow response. These demonstrate, in particular, that this response is switched on asymptotically far downstream from the topography, in contrast to what is often assumed in parameterisation.

Cette thèse porte sur la dynamique des grandes échelles des écoulements géophysiques turbulents, en particulier sur leur organisation en écoulements parallèles orientés dans la direction est-ouest (jets zonaux). Ces structures ont la particularité d'évoluer sur des périodes beaucoup plus longues que la turbulence qui les entoure. D'autre part, on observe dans certains cas, sur ces échelles de temps longues, des transitions brutales entre différentes configurations des jets zonaux (multistabilité). L'approche proposée dans cette thèse consiste à moyenner l'effet des degrés de liberté turbulents rapides de manière à obtenir une description effective des grandes échelles spatiales de l'écoulement, en utilisant les outils de moyennisation stochastique et la théorie des grandes déviations. Ces outils permettent d'étudier à la fois les attracteurs, les fluctuations typiques et les fluctuations extrêmes de la dynamique des jets. Cela permet d'aller au-delà des approches antérieures, qui ne décrivent que le comportement moyen des jets.Le premier résultat est une équation effective pour la dynamique lente des jets, la validité de cette équation est étudiée d'un point de vue théorique, et les conséquences physiques sont discutées. De manière à décrire la statistique des évènements rares tels que les transitions brutales entre différentes configurations des jets, des outils issus de la théorie des grandes déviations sont employés. Des méthodes originales sont développées pour mettre en œuvre cette théorie, ces méthodes peuvent par exemple être appliquées à des situations de multistabilité. / This thesis deals with the dynamics of geophysical turbulent flows at large scales, more particularly their organization into east-west parallel flows (zonal jets). These structures have the particularity to evolve much slower than the surrounding turbulence. Besides, over long time scales, abrupt transitions between different configurations of zonal jets are observed in some cases (multistability). Our approach consists in averaging the effect of fast turbulent degrees of freedom in order to obtain an effective description of the large scales of the flow, using stochastic averaging and the theory of large deviations. These tools provide theattractors, the typical fluctuations and the large fluctuations of jet dynamics. This allows to go beyond previous studies, which only describe the average jet dynamics. Our first result is an effective equation for the slow dynamics of jets, the validityof this equation is studied from a theoretical point of view, and the physical consequences are discussed. In order to describe the statistics of rare events such as abrupt transitions between different jet configurations, tools from large deviation theory are employed. Original methods are developped in order to implement this theory, those methods can be applied for instance in situations of multistability.

The sinking of dense shelf waters down the continental slope (or “cascading”) contributes to oceanic water mass formation and carbon cycling. Cascading is therefore of significant importance for the global overturning circulation and thus climate. The occurrence of cascades is highly intermittent in space and time and observations of the process itself (rather than its outcomes) are scarce. Global climate models do not typically resolve cascading owing to numerical challenges concerning turbulence, mixing and faithful representation of bottom boundary layer dynamics. This work was motivated by the need to improve the representation of cascading in numerical ocean circulation models. Typical 3-D hydrostatic ocean circulation models are employed in a series of numerical experiments to investigate the process of dense water cascading in both idealised and realistic model setups. Cascading on steep bottom topography is modelled using POLCOMS, a 3-D ocean circulation model using a terrain-following s-coordinate system. The model setup is based on a laboratory experiment of a continuous dense water flow from a central source on a conical slope in a rotating tank. The descent of the dense flow as characterised by the length of the plume as a function of time is studied for a range of parameters, such as density difference, speed of rotation, flow rate and (in the model) diffusivity and viscosity. Very good agreement between the model and the laboratory results is shown in dimensional and non-dimensional variables. It is confirmed that a hydrostatic model is capable of reproducing the essential physics of cascading on a very steep slope if the model correctly resolves velocity veering in the bottom boundary layer. Experiments changing the height of the bottom Ekman layer (by changing viscosity) and modifying the plume from a 2-layer system to a stratified regime (by enhancing diapycnal diffusion) confirm previous theories, demonstrate their limitations and offer new insights into the dynamics of cascading outside of the controlled laboratory conditions. In further numerical experiments, the idealised geometry of the conical slope is retained but up-scaled to oceanic dimensions. The NEMO-SHELF model is used to study the fate of a dense water plume of similar properties to the overflow of brine-enriched shelf waters from the Storfjorden in Svalbard. The overflow plume, resulting from sea ice formation in the Storfjorden polynya, cascades into the ambient stratification resembling the predominant water masses of Fram Strait. At intermediate depths between 200-500m the plume encounters a layer of warm, saline AtlanticWater. In some years the plume ‘pierces’ the Atlantic Layer and sinks into the deep Fram Strait while in other years it remains ‘arrested’ at Atlantic Layer depths. It has been unclear what parameters control whether the plume pierces the Atlantic Layer or not. In a series of experiments we vary the salinity ‘S’ and the flow rate ‘Q’ of the simulated Storfjorden overflow to investigate both strong and weak cascading conditions. Results show that the cascading regime (piercing, arrested or ‘shaving’ - an intermediate case) can be predicted from the initial values of S and Q. In those model experiments where the initial density of the overflow water is considerably greater than of the deepest ambient water mass we find that a cascade with high initial S does not necessarily reach the bottom if Q is low. Conversely, cascades with an initial density just slightly higher than the deepest ambient layer may flow to the bottom if the flow rate Q is high. A functional relationship between S/Q and the final depth level of plume waters is explained by the flux of potential energy (arising from the introduction of dense water at shallow depth) which, in our idealised setting, represents the only energy source for downslope descent and mixing. Lastly, the influence of tides on the propagation of a dense water plume is investigated using a regional NEMO-SHELF model with realistic bathymetry, atmospheric forcing, open boundary conditions and tides. The model has 3 km horizontal resolution and 50 vertical levels in the sh-coordinate system which is specially designed to resolve bottom boundary layer processes. Tidal effects are isolated by comparing results from model runs with and without tides. A hotspot of tidally-induced horizontal diffusion leading to the lateral dispersion of the plume is identified at the southernmost headland of Spitsbergen which is in close proximity to the plume path. As a result the lighter fractions in the diluted upper layer of the plume are drawn into the shallow coastal current that carries Storfjorden water onto the Western Svalbard Shelf, while the dense bottom layer continues to sink down the slope. This bifurcation of the plume into a diluted shelf branch and a dense downslope branch is enhanced by tidally-induced shear dispersion at the headland. Tidal effects at the headland are shown to cause a net reduction in the downslope flux of Storfjorden water into deep Fram Strait. This finding contrasts previous results from observations of a dense plume on a different shelf without abrupt topography. The dispersive mechanism which is induced by the tides is identified as a mechanism by which tides may cause a relative reduction in downslope transport, thus adding to existing understanding of tidal effects on dense water overflows.