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.

The thesis deals with the manifestation of coupling processes of various timescales in the middle atmosphere. Longer and shorter timescales are represented here by the 11-year solar cycle (SC) and orographic gravity waves (oGWs) considered on the intraseasonal timescale of the north hemisphere winter, respectively. The first two chapters deal with the application of rigorous attribution the variability of temperature, ozone and circulation characteristics in the stratosphere and lower mesosphere with regard to the SC using multiple nonlinear techniques (support vector regression and neural networks) besides the multiple linear regression approach. The aliasing of the SC with volcanic eruptions or the El Niňo Southern Oscillation is qualitatively assessed and its impact on conclusions about the top-down coupling mechanisms discussed. The last chapter examines the role of parametrized oGWs in the lower stratosphere. The Himalayan hotspot reveals common features with sudden stratospheric warmings such as the residual circulation amplification leading to a warming and ozone enrichment in the polar latitudes of the lower stratosphere.

L'Océan Austral est une zone clef pour la circulation océanique tant à cause de l'intensité du courant circumpolaire antarctique qu'en tant que région de formation des masses d'eaux abyssales de l'océan global. Pour modéliser l'océan et prévoir les changements climatiques futurs, il est important de comprendre les processus de mélange diapycnal qui lient ces eaux abyssales aux couches supérieures. Dans l'Océan Austral, des courants profonds et intenses s'écoulent sur une topographie accidentée, ce qui génère des ondes internes de relief très énergétiques. Actuellement, la dissipation de l'énergie induite par ces ondes de relief est la candidate principale pour expliquer les forts taux de mélange observés à ces latitudes. L'objet du présent travail de thèse est de comprendre comment les ondes internes de relief sont dissipées et affectent la circulation et le mélange diapycnal dans l'océan abyssal. Nous examinons l'impact de ces ondes sur le mélange profond au moyen d'une combinaison d'expertise de terrain, de simulations non hydrostatiques bi-dimensionnelles et de calculs théoriques. Sur la gamme de paramètres étudiés, nous montrons, en présence des ondes de relief, une intensification du taux de dissipation d'énergie cinétique turbulente sur une profondeur de 1000 m au-dessus de la topographie, atteignant typiquement ~20 mW/m2. Nous montrons également comment les ondes participent à des interactions triadiques impliquant des oscillations inertielles qui sont amplifiées par intéractions résonantes contrôlées par les ondes de relief. Finalement, nous préparons de futures études tri-dimensionnelles en concevant un cadre numérique et en décrivant des outils théoriques adaptés à ce problème. Nos résultats préliminaires en trois dimensions montrent qui le confinement méridien de la topographie réduit significativement l'émissions d'ondes internes de relief. / The Southern Ocean plays a key role in global ocean circulation by connecting the major ocean basins with the intense Antarctic Circumpolar Current and as a formation region for abyssal water masses of the global ocean. Understanding the diapycnal mixing processes that link these abyssal waters to the overlying layers is essential both for ocean modelling and for predicting future climate change. In the Southern Ocean, deep reaching currents impinge on rough topography and create highly energetic internal lee waves. The dissipation of the energy of these internal lee waves is the main candidate for explaining the high mixing rates between waters of different densities observed at these latitudes. The purpose of this study is to understand the fate of the internal lee wave energy and how it affects the circulation and diapycnal mixing in the abyssal ocean. We first study the impact of internal lee waves on deep mixing with the combination of field expertise, two-dimensional non hydrostatic numerical simulations and theoretical developments. Over the range of parameters studied, an enhanced bottom turbulent kinetic energy dissipation is observed in the bottom 1000 m, typically reaching $sim$ 20 mW.m$^{-2}$. We further show that internal lee waves undergo non-dissipative wave-wave interactions that can be rationalized as resonant triad interactions between the bottom emitted internal lee waves, inertial oscillations and linear combinations of these two waves. We then build a three-dimensional model configuration and specific diagnostic methods that pave the way for future investigations in three dimensions. Preliminary results with the three-dimensional numerical configuration show that the meridional confinement of the topography notably reduces the emission of internal lee waves.