The main purpose of this thesis is to use state of the art computational fluid dynamics techniques to solve the problem of water-wind waves which are related to air-sea interaction. In general, air-sea interaction is studied in a de-coupled manner where both air and water phases are separate and the water phase is either considered as a smooth or rough wall which is stationary or moving. However, in real ocean waves the air and water are coupled. Mass, momentum, heat and energy exchange takes place mostly on the surface waves and this process is culminated when the waves break. Numerical modelling to study these processes requires the solution of the full Navier-Stokes equations along with capturing the interface boundary of the wave with high accuracy, thereby helping us to understand the physical processes taking place on the air-water interface and improve current wave modelling techniques. Our primary motivation is two fold: (1) to investigate the accuracy and reliability of the state of the art numerical techniques available for simulating free surface flows and model air-water wave interaction and (2) to study various near surface physical processes taking place at the transient, viscous, rotational and nonlinear air-water wave interface and understand its effects on the momentum and energy exchange in wind waves. The work presented in this thesis investigates a numerical model to solve the full Navier Stokes equations required to model transient, viscous, rotational and nonlinear water waves. The first step in the process is to model the water waves when the average wind speed is zero. Various other physical aspects related to wave dynamics are discussed for intermediate depth and deep water waves with different steepnesses. They are compared with earlier experimental and theoretical works available in order to verify the accuracy of the model . The second step is to model these water waves in the presence of wind blowing at different speeds and analyze its effects on various near surface physical properties and its effect on the motions in the air and underlying water. The other purpose of this thesis is to investigate some very interesting aspects related to wave dynamics such as vorticity and shear stress which are little studied due to complexities surrounding near surface flow measurements and the lack of an accurate analytical solution. The current work provides a tool for the application of CFD techniques to reliably predict wind-wave interaction by using numerical modelling techniques used in multi-phase flow environments. The accuracy and convergence of the numerical technique used in this thesis is illustrated by comparing the numerical results with analytical and theoretical results available. The technique is demonstrated to be accurate in the simulation of twodimensional flows where turbulent effects are negligible. At higher wind speeds, the use of suitable turbulence closure models is recommended. The main conclusions drawn from the study are: (1) accurate simulation of two and three dimensional, unsteady, viscous and nonlinear water waves is possible with current CFD techniques; (2) The role played by shear stress and vorticity in the wind wave interaction is important and cannot be ignored; (3) the vertical velocity gradients observed inside the water in intermediate depth water waves are found to be stronger than deep water waves; and (4) the effect of the bottom boundary on the magnitude of free surface vorticity is not found to be high.

The propagation of planetary, or Rossby, waves is studied under the effects of different atmospheric couplings. First, analytical matchings are formulated in which a Rossby wave is coupled to different thermodynamical atmospheres, from a simple heat flux condition to the inclusion of an atmospheric energy balance model. The effects on the vertical structure and phase speed of the first modes are negligible. However, it is shown that for the latter case an unstable mode appears. This growing mode, of decadal period and growth rate, has no physical source of energy and therefore is a result of the oversimplified atmosphere employed. In fact, adding physics to the atmospheric model results in a gradual disappearance of the instability. The possibility of observing similar unphysical modes in climate studies, where oversimplified models are adopted, is raised. Next, a quasi-geostrophic coupled model is used in order to analyse the oceanic Rossby wave characteristics under the influence of a full atmosphere. The idealised eddy-resolving model consists of an ocean basin underneath a channel atmosphere, and different configurations for the oceanic component are used. The Rossby waves are observed to propagate faster than both the classical linear theory (unperturbed solution) and the phase speed estimates when the effect of the zonal mean flow is added (perturbed solution). Moreover, using statistical eigentechniques, a coupled Rossby wave is identified, bearing the characteristics of the coupled mode proposed by Goodman and Marshall (1999). It is argued that the atmospheric coupling is capable of adding an extra speed up to the wave; in fact, when the waves are simply forced, their propagation speed approaches the perturbed solution. The waves are observed to break into faster waves, as suggested by LaCasce and Pedlosky (2004), although their resistance to dissipation and instabilities processes is enhanced by the atmospheric coupling, which provides extra energy to the initial wave during its propagation. The development of a coupled Rossby wave is found to be possible in a basin of the dimensions of both the Pacific and the Atlantic ocean, and its characteristics and strength vary little when the tridimensional accuracy of the ocean is increased.

Recent spectroscopic observations of transiting exoplanets have permitted the derivation of the thermal structure and molecular abundances of H₂O, CO, CO₂, CH₄, metallic oxides and alkali metals in these extreme atmospheres. Here, for the first time, a fully-fledged retrieval algorithm has been applied to exoplanet spectra to determine the thermal structure and composition. The development of a suite of radiative transfer and retrieval tools for exoplanet atmospheres is described, building upon an optimal estimation retrieval algorithm extensively used in solar system studies. Firstly, the collection of molecular line lists and the pre-tabulation of the absorption coefficients (k-distribution tables) for high temperature application are discussed. Secondly, the best-fit spectra for hot Jupiters are demonstrated and discussed case by case. Available sets of primary and secondary transit observations of exoplanets are used to retrieve atmospheric properties from these spectra, quantifying the limits of our knowledge of exoplanetary atmospheres based on the current quality of the data. The contribution functions and the vertical sensitivity to the molecules are fully utilised to interpret these spectra, probing the structure and composition of the atmosphere. Finally, the retrievals provide our best estimates of the thermal and compositional structure to date, using the covariance matrices to properly assess the degeneracy between different parameters and the uncertainties on derived quantities for the first time. This sheds light on the range of diverse interpretations offered by other authors so far, and allows us to scrutinise further atmospheric features by maximising the capability of the current retrieval algorithm and to demonstrate the need for broadband spectroscopy from future missions.