Waves with periods shorter than the inertial period exist in the atmosphere (as inertia- gravity waves) and in the oceans (as Poincare and internal gravity waves). Such waves owe their origin to various mechanisms, but of particular interest are those arising either from local secondary instabilities or spontaneous emission due to loss of balance. Previous researchers have studied these phenomena in the laboratory, both in the mechanically-forced and the thermally-forced rotating annulus. Their generation mechanisms, especially in the latter system, have not yet been fully understood. This project aims to change that. Firstly, we present a laboratory investigation using the two layer mechanically-forced annulus. We perform a new series of experiments in which we combine an existing polarised light altimetry technique with particle imaging velocimetry. This necessi- tated a substantial rebuild of the apparatus. The new vessel enables us to measure the flow in one of the layers directly, and thus investigate the validity of a torque bal- ance calculation used by previous experimenters that was hitherto unverified. We use these results to discuss the possibility that the inertia-gravity waves seen in the two layer annulus might have been generated by a shear instability; either that of Holm- boe, or an Ekman layer instability. Our investigation suggests that whilst Holmboe's instability is unlikely to be the cause, a localised Ekman layer instability is a possible generation mechanism for the short waves seen in earlier experiments. Secondly, we perform a numerical investigation using a fully nonlinear, finite-difference, 3D Boussinesq N avier-Stokes model of the rotating thermal annulus. The model pre- dicts the generation of short waves from 'wavemaker' regions determined by strong shear and downwelling near the inner cylinder. These then propagate into the geo- strophic interior of the fluid as inertia-gravity waves, where they have been detected in previous laboratory experiments. We then show how these wavemakers are con- sistent with being due to a localised thermal boundary layer instability, which has a number of similarities to the Ekman layer instability of the two-layer annulus. Such a mechanism also has many similarities with those responsible for launching small- and meso-scale inertia-gravity waves in the atmosphere from fronts and local convection.

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The Met Office uses the NAME dispersion model to solve stochastic differential equations (SDEs) for predicting the transport and spread of atmospheric pollutants. Time stepping methods for this SDE dominate the computation time. In particular the slow convergence of the Monte Carlo Method imposes limitations on the accuracy with which predictions can be made on operational timescales. We review the theory of both the Standard and Multi Level Monte Carlo Methods, and in particular the complexity theorems discussed in [9] in a more general context. We then argue how it can potentially give rise to significant gains for this problem in atmospheric dispersion modelling. To verify these theoretical arguments numerically, we consider two model problems; a simplified problem which corresponds to homogeneous turbulence and is used by the Met Office for long term predictions, as well as a full non-linear model problem close to that used by the Met Office for atmospheric dispersion modelling. For both model problems we performed numerical tests in which we observed significant speed-up as a result of the implementation of the Multi Level Monte Carlo Method. The numerically observed convergence rates are also confirmed by a full theoretical analysis for the simplified model problem.

The study of boundary layer flow through a forest canopy on complex terrain has, until recently, been limited to modelling and laboratory studies. This thesis presents a unique set of field measurements from within and above a canopy situated on a ridge. A climatological study of the observed dataset is presented to identify the significant fea- tures of these flows that differentiate them from air flows above and within a homogeneous canopy on flat terrain. The ridge is found to impact on the flows in the following ways. On the summit the velocity profile resembles that of a canopy profile on flat terrain with little variation in wind.speed below the canopy and an obvious inflection point at the canopy top. On the windward slope, the inflection point disappears. Significant amounts of -u'w' at the canopy top indicates that turbulent mixing acts strongly to transport higher mo- mentum air down into the canopy, which smooths the layer of shear. The profile on the lee slope is dependent on the size of a separation region that can develop on the lee slope of the forested ridge. The direction of the mean wind within the canopy on the lee slope is dependent on the hill-induced pressure gradient, which tends to drive a reversed flow up the lee slope, and on the turbulent mixing which tends to drive the flow down-slope through the mixing of higher momentum air from above the canopy. If the hill slope is sufficiently large (so the pressure gradient is large), or the canopy is sufficiently deep (so that turbulence is unable to mix the higher momentum air all the way to the bottom), then flow separation can occur. Case studies are presented to investigate the formation and development of the separation region on the lee slope of the forested ridge. The presence of a flow separation region is observed to extend the width of the dynamic pressure profile such that, as the separation region expands up the lee slope towards the summit, the minimum is forced back to the upwind edge of the separation region. Large scale separation is observed on the ridge, whereby the separation region extends beyond the top of the canopy. Within the separation region, there is little variation in wind speed or vertical momentum flux with height as the inflection point is elevated to the top of the separation region. Comparisons between the observed case studies and model simulations are made to quan- tify the success of the model at simulating canopy air flows over complex terrain. The model is found to successfully capture the main features the these flows. Areas where the model was less successful are attributed to the inhomogeneous nature of the canopy and the terrain at the field site, and to the low resolution of the model.

Internal gravity waves which propagate upwards from the lower atmosphere transport energy and momentum into the middle and upper atmosphere. As these waves dissipate, they alter the dynamics and composition of the background atmosphere. Changes in the background also affect the dissipation of these waves. Through this interplay, gravity waves couple the lower and upper atmosphere. Recent improvements in our understanding of gravity waves have allowed detailed physical representations of these waves to be included in global-scale atmospheric models. Three models have been developed for this study which are used to examine the role of gravity waves in the dynamics of the middle and upper atmosphere over a range of time-scales. The effects of the solar sunspot cycle on gravity waves in the middle atmosphere are explored. Changes in the wave-induced wind variance of up to 10 % are simulated in the mesosphere. It is shown that a strong change in the tropospheric gravity-wave source could explain observed variability in gravity waves in this region, but changes in the mesospheric winds also play a crucial role in the model results. Varying the amplitude of the lower atmosphere gravity-wave source affects gravity-wave drag and the residual circulation. These are shown to influence conditions in the stratosphere and can alter the strength of sudden warmings. This has important consequences for the whole atmosphere. The interaction between gravity wave-drag and the diurnal tide is investigated using a coupled middle atmosphere and thermosphere model. This is shown to have a strong influence on dynamics and airglow emissions in the equatorial MLT region. Further constraint of the lower-atmosphere gravity waves and time dependent propagation effects are needed to improve our understanding of the role which gravity waves play in the dynamical coupling of the atmosphere.

The periods of time-varying turbulence in the atmospheric boundary layer, i.e.\ the morning and evening transitions, are often overlooked or highly idealised by dispersion models. These transitions make up a significant portion of the diurnal cycle and are known to affect the spread of pollution due to the properties of turbulence in the residual and stable layers, resulting in phenomena such as lofting, trapping, and fumigation.\\ Two main simulation techniques are presented for the purpose of modelling the dispersion of passive tracers in both convective and evening transitional boundary layers: Lagrangian stochastic (LS) modelling for 1D, inhomogeneous, non-stationary turbulence; and large-eddy simulation (LES) with a particle model tracing pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent sub-grid scale motions.\\ In the convective boundary layer, LS models more accurately representing the state of turbulence, and including the effect of skewness, are shown to produce dispersion results in closer agreement with LES. By considering individual particle trajectories, a reflective top boundary in LS models is shown to produce un-physical, sharp changes in velocity and position. By applying a correction to the vertical velocity variance based on representing the stable potential temperature gradient above the boundary layer, particles are contained within the boundary layer in a physically accurate way. \\ An LS model for predicting dispersion in time-varying, skewed turbulence is developed and tested for various particle releases in transitional boundary layers with different rates of decay, showing an improvement in accuracy compared with previous LS models. Further improvement is made by applying a correction to the vertical velocity variance to represent the effect of a positive potential temperature gradient developing over the course of the transition. Finally, a developing stable boundary layer is shown to have a significant trapping effect on particles released near the surface. \\