The majority of internal gravity wave energy in the ocean is produced by tidal flow over bottom topography. Regions of critical topography, where the topographic slope is equal to the slope of the internal gravity waves, is often believed to contribute most significantly to the radiated internal gravity wave power. Here, we present 2D computational studies of internal gravity wave generation by tidal flow over several types of topographic ridges. We vary the criticality parameter [epsilon], which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification and topographic slope, which allows to study subcritical ([epsilon] < 1), critical ([epsilon] = 1), and supercritical ([epsilon] > 1) topography. This parameter variation allows us to explore a large range of criticality parameter, namely 0.1< [epsilon] < 10, as well as beam slope S, 0.05< S < 10. As in prior work [Zhang et al., Phys. Rev. Lett. (2008)], we observe resonant boundary currents for [epsilon] = 1. However, we find that the normalized radiated power monotonically increases with internal wave beam slope. We show that an appropriate normalization condition leads to a universal scaling of the radiated power that is proportional to the inverse of the beam slope 1/S and the tidal intensity I[subscript tide], except near [epsilon] = 1 where the behavior undergoes a transition. We characterize this transition and the overall scaling with the criticality parameter f([epsilon]), which is weak compared to the scalings mentioned before and only varies by a factor of two over the entire range of criticality parameter that we explored. Our results therefore suggest that estimates of the ocean energy budget must account for the strong scaling with the local beam slope, which dominates the conversion of tidal motions to internal wave energy. Thus we argue that detailed characterization of the stratification in the ocean is more important for global ocean models than high-resolution bathymetry to determine the criticality parameter. / text

Since the first discovery of an extrasolar planet around a solar-type star, observers have detected over 500 planets outside the solar system. Many of these planets have Jovian masses and orbit their host stars in orbits of only a few days, the so-called 'Hot Jupiters'. At such close proximity to their parent stars, strong tidal interactions between the two bodies are expected to cause significant secular spin-orbit evolution. This thesis tackles two problems regarding the tidal evolution of short-period extrasolar planets. In the first part, we adopt a simple model of the orbit-averaged effects of tidal friction, to study the tidal evolution of planets on inclined orbits. We also analyse the effects of stellar magnetic braking. We then discuss the implications of our results for the importance of Rossiter-Mclaughlin effect observations. In the second part, we study the mechanisms of tidal dissipation in solar-type stars. In particular, internal gravity waves are launched at the interface of the convection and radiation zones of such a star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star is studied, primarily using numerical simulations, in both two and three dimensions. We find that the waves undergo instability and break above a critical amplitude. A model for the tidal dissipation that results from this process is presented, and its validity is verified by numerical integrations of the linear tidal response, in an extensive set of stellar models. The dissipation is efficient, and varies by less than an order of magnitude between all solar-type stars, throughout their main-sequence lifetimes, for a given planetary orbit. The implications of this mechanism for the survival of short-period extrasolar planets is discussed, and we propose a possible explanation for the survival of all of the extrasolar planets currently observed in short-period orbits around F, G and K stars. We then perform a stability analysis of a standing internal gravity wave near the centre of a solar-type star, to understand the early stages of the wave breaking process in more detail, and to determine whether the waves are subject to weaker parametric instabilities, below the critical amplitude required for wave breaking. We discuss the relevance of our results to our explanation for the survival of short-period planets presented in the second part of this thesis. Finally, we propose an alternative mechanism of tidal dissipation, involving the gradual radiative damping of the waves. Based on a simple estimate, it appears that this occurs even for low mass planets. However, it is in conflict with current observations since it would threaten the survival of all planets in orbits shorter than 2 days. We discuss some hydrodynamic instabilities and magnetic stresses which may prevent this process.

The effects of propagation of a short internal gravity wave through an inertia wave on internal wave stability is analyzed and parameterized. The interactions are specifically between a short wave packet and a large inertia wave packet. The short wave packet is a wave bounded with a Gaussian envelope with high frequencies and scales in the hundreds of meters horizontally and tens of meters vertically. The inertia wave packet is also an enveloped wave but with frequencies close to the rotation of the earth and scales in the thousands of meters in the horizontal and hundreds of meters in the vertical. The wave-wave interactions are modeled using ray theory and 2d non-linear numerical models. Ray tracing is used because it is less computationally expensive, however it fails at regions of strong refraction also known as caustics. To measure stability the steepness is calculated from the 2d non-linear methods and it is compared with estimates found in the linear theory. It is determined that the estimates of the short wave steepness from linear theory are qualitatively comparable. A quantifiable comparison, although more difficult, resulted in adjustment factors to the ray tracing results. It is also found that for the particular cases modeled, convective instabilities are predominant and the influence of the shear exerted by the large inertia wave is insignificant. Instability time scales are included in the stability analysis and estimates of overturning and wave-breaking are developed for different wave-wave interactions. From the stability analysis it is found that in general the faster the short wave propagates the more likely it is to conform to both of the conditions required for wave breaking (i.e presence of instabilities and instability time scales longer than the timescale of the short wave).

La dynamique des écoulements géophysiques planétaires est fortement influencée par des processus physiques souvent non résolus par les modèles numériques de circulation générale. Il est essentiel de comprendre les mécanismes physiques sous-jacents pour paramétrer l’effet des petites échelles sur les grandes. Dans cette thèse, nous étudions un problème emblématique d’interactions entre ondes et écoulements moyens : la dynamique des écoulements zonaux forces par des ondes internes de gravite. Une manifestation remarquable de ces interactions est l’oscillation quasi-biennale (QBO) des vents équatoriaux dans l’atmosphère terrestre. Dans un premier temps, nous décrivons une transition vers le chaos dans un modèle quasi-linéaire classique du QBO. Nous montrons que ces bifurcations persistent dans des simulations numériques directes. A l’aune de ces résultats, nous proposons une interprétation de l’observation d’une rupture inattendue de la périodicité du QBO en 2016. Le mécanisme de génération d’écoulements moyens par les ondes dans les fluides stratifies nécessite la prise en compte d’effets dissipatifs. Il s’agit d’un phénomène analogue au "streaming" acoustique. Dans un second temps nous exploitons cette analogie en étudiant la génération d’écoulements moyens par les ondes internes proche d’une paroi, a l’aide d’approches asymptotiques multi échelles. Finalement, nous proposons une approche inertielle pour décrire l’émergence spontanée d’écoulements vorticaux en présence d’ondes : nous appliquons les outils de mécanique statistique pour calculer la partition d’énergie entre petites et grandes échelles dans le modèle d’eau peu profonde. / The dynamics of planetary-scale geophysical flows is strongly influenced by physicalprocesses, mostly unresolved by general circulation numerical models. To parametrisethe coupling between small and large scales, it is essential to understand the underlying physical mechanisms. In this thesis, we study an emblematic problem of interactions between waves and mean flows: the dynamics of zonal flows forced by internal gravity waves. A striking manifestation of these interactions is the quasi-biennial oscillation (QBO) of equatorial winds in the Earth’s atmosphere. First, we describe a transition to chaos in a classical quasilinear model of the QBO and show that these bifurcations persist in direct numerical simulations. Based on these results, we suggest an interpretation for the observation of the unexpected periodicity disruption of the QBO in 2016. The mechanism by which mean flows are generated by waves in stratified fluids requires the consideration of dissipative effects. This phenomenon is analogous to acoustic "streaming". In a second time, we exploit this analogy to study the generation of mean flows by internal gravity waves close to a wall, using multi-scale asymptotic approaches. Finally, we propose an inertial approach to describe the spontaneous emergence of vortical flows in the presence of waves: we apply the tools of statistical mechanics to calculate the partition of energy between small and large scales in the shallow-water model.

Les ondes internes sont produites par suite de l’équilibre dynamique entre les forces de flottabilité et la gravité quand une particule de fluide est déplacée verticalement dans un milieu stratifié stable. Les systèmes géophysiques tels que océan et l’atmosphère sont naturellement stratifiés et donc favorables à la propagation des ondes internes. En outre, ces deux environnements stockent une grande quantité de particules tant dans leur intérieur que sur les bords. Par conséquent, les ondes internes et les particules vont inévitablement interagir dans ces systèmes. Au cours de ce travail, des expériences exploratoires sont réalisées pour étudier le transport par érosion des particules, généré par les ondes internes. Afin de déterminer un seuil de transport, les propriétés particulières des réflexions d’ondes internes («réflexion critique ») sont utilisées pour augmenter l’intensité du champ d’ondes à la surface de réflexion. Une méthode a été développée en collaboration avec une équipe de traitement du signal pour améliorer la détermination des composantes de l’onde impliquées dans une réflexion quasi critique. Cela nous a permis de comparer nos résultats expérimentaux avec une théorie de la réflexion critique, montrant un bon accord et permettant d’extrapoler ces résultats à des expériences au-delà de la nôtre et à des conditions océaniques. Nous avons aussi étudié l’interaction des ondes internes avec une colonne de particules en sédimentation. Deux effets principaux ont été observés : la colonne oscille autour d’une position d’équilibre, et elle est déplacée dans son ensemble. La direction du déplacement de la colonne est expliquée par le calcul de l’effet de la dérive Lagrangienne produite pour des ondes. Cet effet pourrait également expliquer la dépendance en fréquence du déplacement. / Internal waves are produced as a consequence of the dynamic balance between buoyancy and gravity forces when a particle of fluid is vertically displaced in a stably stratified environment. Geophysical systems such as ocean and atmosphere are naturally stratified and therefore suitable for internal waves propagation. Furthermore, these two environments stock a vast amount of particles at their boundaries and in their bulk. Therefore, internal waves and particles will inexorably interact in these systems. In this work, exploratory experiments are performed to study wave generated erosive transport of particles. In order to determine a transport threshold, the peculiar properties of internal waves (“critical reflection”) are employed to increase the intensity of the wave field at the boundaries. A method was developed in collaboration with a signal processing team to improve the determination of the wave components involved in near-critical reflection. This method enabled us to compare our experimental results with a theory of critical reflection, showing good agreement and allowing to extrapolate these results to experiments beyond ours and to oceanic conditions. In addition, we study the interaction of internal waves with a column of particles in sedimentation. Two main effects are observed: the column oscillates around an equilibrium position, and it is displaced as a whole. The direction of the displacement of the column is explained by computing the effect of the Lagrangian drift of the waves. This effect could also explain the frequency dependence of the displacement.

Internal gravity waves play a fundamental role in the dynamics of stably stratified regions of the atmosphere and ocean. In addition to the radiation of momentum and energy remote from generation sites, internal waves drive vertical transport of heat and mass through the ocean by wave breaking and the mixing subsequently produced. Identifying regions where internal gravity waves contribute to ocean mixing and quantifying this mixing are therefore important for accurate climate and weather predictions. Field studies report significantly enhanced measurements of turbulence near 'rough' ocean topography compared with those recorded in the ocean interior or near more gradually varying topography (e.g. Toole et al. 1997, J. Geophys. Res. 102). Such observations suggest that interaction of waves with rough topography may act to skew wave energy spectra to high wavenumbers and hence promote wave breaking and fluid mixing. This thesis examines the high wavenumber scatter and spatial partitioning of wave energy at 'rough' topography containing features that are of similar scales to those characterising incident waves. The research presented here includes laboratory experiments using synthetic schlieren and PIV to visualise two-dimensional wavefields produced by small amplitude oscillations of cylinders within linear salt-water stratifications. Interactions of wavefields with planar slopes and smoothly varying sinusoidal topography are compared with those with square-wave, sawtooth and pseudo knife-edge profiles, which have discontinuous slopes. Far-field structures of scattered wavefields are compared with linear analytical models. Scatter to high wavenumbers is found to be controlled predominantly by the relative slopes and characterising length scales of the incident wavefield and topography, as well as the shape and aspect ratio of the topographic profile. Wave energy becomes highly focused and the spectra skewed to higher wavenumbers by 'critical' regions, where the topographic slope is comparable with the slope of the incident wave energy vector, and at sharp corners, where topographic slope is not defined. Contrary to linear geometric ray tracing predictions (Longuet-Higgins 1969, J. Fluid Mech. 37), a significant back-scattered field can be achieved in near-critical conditions as well as a forward scattered wavefield in supercritical conditions, where the slope of the boundary is steeper than that of the incident wave. Results suggest that interaction with rough benthic topography could efficiently convert wave energy to higher wavenumbers and promote fluid mixing in such ocean regions.

This thesis is concerned with the role of internal gravity waves (IGWs) in the stratospheric dynamics and variability demonstrating the effect of spatiotemporal distribution of their activity on the stratospheric dynamics and transport. The first part introduces a theoretical overview of the most recent as well as classical approaches used for description of the wave-mean interaction in the middle atmosphere. Methodology for an IGW analysis from the GPS radio occultation density data is described in the next chapter and the advantages of utilization of density data are listed. The third chapter presents results describing the peculiar dynamics and anomalous IGW activity in the Eastern Asia/Northern Pacific region. An important part is dedicated to a discussion of accuracy limits and usability of different IGW activity proxies. The possible impact of the localized IGW activity is investigated using a mechanistic middle and upper atmosphere model in the last chapter. Sensitivity simulations are used to demonstrate an important role of the spatial distribution of IGW activity for a formation of planetary waves and for the longitudinal variability of the Brewer-Dobson circulation. Implications for the middle atmospheric and climate change research are discussed along with consequences for parameterizations of...

Internal gravity waves (GWs) are an important component of the atmospheric dynamics, significantly affecting the middle atmosphere by momentum and energy transport and deposition. In order to be able to improve global circulation models, in which the majority of the GW spectrum is not resolved, it is necessary to quantify their effects as precise as possible. We study GWs in a high-resolution simulation of the WRF model around Southern Andes, Antarctic Peninsula and South Georgia Island. We analyse a Gaussian high-pass filter method for separation of GWs from the basic flow. To overcome an observed problem of dependence of the method on a cutoff parameter, we propose an improved method that determines the parameter at each time step from the horizontal kinetic energy spectrum. The differences between the methods are further examined using the horizontal kinetic energy spectrum, vertical potential energy spectrum and forcing to the divergence equation evaluated by the active wind method, which is a recent theory-based method that divides the flow into a balanced flow and a perturbation field. The results suggest that the high-pass filter method does not produce correct results for time periods with strong wave activity.

The present work combines experimental and numerical analyses to improve current understanding of turbulence in stably stratified flows. An extensive literature review is presented on the mechanisms governing turbulence under stratified conditions, with a special focus on the Richardson number parameter, as it is often adopted as a switch to turn turbulence modelling on/off. Anisotropization of turbulence is investigated, as it is found to be an important mechanism for turbulence survival at any Richardson number, but usually overlooked in turbulence parameterizations. For this purpose, an experimental dataset previously collected over an Alpine glacier is used, with a focus on the anisotropy of the Reynolds stress tensor, as the scientific community has recently shown improvements in the description of the atmospheric surface layer by taking this aspect into account. Different sources leading stresses to deviate from the isotropic limit are explored, as well as energy exchanges across scales and between kinetic and potential reservoirs, in order to identify the main processes that should be included in turbulence parameterizations to properly represent anisotropic turbulence under stable conditions. High-resolution numerical simulations are then performed with the Weather Research and Forecasting (WRF) model to evaluate different PBL parameterizations in reproducing specific stable atmospheric conditions developing over complex terrain, and their influence on the local circulation. For this purpose, two wintertime case studies in a basin-like area of an Alpine valley are investigated. Both are fair-weather episodes with weak synoptic forcing and well-developed diurnal local circulations, differing by the thermal stratification in the basin. In particular, the influence of thermal stratification on the outbreak of a valley-exit wind coming from a tributary valley is investigated, and the influence of such type of flows on turbulence anisotropy in stably stratified conditions is discussed for future investigations.

Une étude numérique de la dynamique d'ondes internes de gravité en fluide stablement stratifié est menée. On décrit un algorithme pseudo-spectral<br />parallèle permettant d'intégrer les équations de Navier-Stokes sur une machine paralèele. En deux dimensions d'espace, on analyse la dynamique d'un<br />champ d'ondes internes propagatives, d'amplitude modérée et initialement plan et monochromatique. Le champ d'ondes est instable et déferle. Le déferlement produit une turbulence de petites échelles spatiales influencées par la stratification. L'étude<br />est étendue au cas tridimensionnel, plus réaliste. En trois dimensions, on étudie le même champ d'ondes internes, que l'on perturbe par un bruit infinitésimal ondulatoire tridimensionnel, mais on considère des ondes statiquement stables et<br />instables (grandes amplitudes). On montre que le déferlement d'une onde interne est un processus intrinsèquement tridimensionnel, y compris pour les ondes de faible amplitude. La tridimensionalisation du champ d'ondes s'opère dans les zones de l'espace où le champ de densité devient statiquement instable. L'effondrement gravitationnel d'une zone est de structure transverse au plan de propagation de l'onde. Les effets de la turbulence des petites échelles sur la production de la composante non propagatrice de l'écoulement, le mode de vorticité potentielle et la production d'un écoulement moyen, permet de conclure que seule une petite proportion de l'énergie mécanique initiale est convertie sous ses deux formes, la majeure partie étant dissipée par la dissipation visqueuse et conduction thermique. On reconsidère le mode de vorticiée potentielle par une approche Hamiltonienne non-canonique du fluide parfait stratifié. La dérivation d'un système de dynamique modifiée permet d'étudier la relaxation d'un écoulement stratifié, conservant sa vorticité potentielle et sa densité, vers un état stationnaire d'énergie minimale, correspondant au mode de vorticité potentielle.