# D.Phil. theses in the group since 2003

### Ruan, T. (2015), "The Climate of Mars from Assimilations of Spacecraft Data"

The Mars climate has been explored using two reanalysis datasets based on combining spacecraft observations of temperature and dust with the UK version of the LMD1 Mars GCM. The semiannual oscillation (SAO) of zonal-mean zonal wind was studied using the existing Mars Analysis Correction Data Assimilation reanalysis during Mars Years (MYs) 24-27. The SAO of zonal-mean zonal wind was shown to exist and extend over a wide range of latitudes. The dynamical driving processes of the SAO in the tropics were investigated, and the forcing due to meridional advection appeared to be the main contributor to the SAO. The study also highlighted some phenomena associated with perturbations of the global circulation during the MY 25 global dust storm (GDS). The meridional advection term was shown to be weaker in the first half of GDS year MY 25 than in the following year, but the forcing due to meridional advection and westward thermal tides both appeared to intensify during the MY 25 GDS.

The capabilities of the Mars data assimilation system were also extended in this thesis, 1) to represent dynamic dust lifting and dust transport during the assimilation and 2) to assimilate measurements of the dust vertical distribution. The updated reanalysis was then used to study several major dust events during MY28-29. It proved able to reproduce a southward-moving regional dust storm without the overwhelming assistance of the assimilation. Dust devil lifting was found to at least partly provide the initial pattern of dust of this moving dust storm. The cold anomaly of the cooling zone beneath this dust storm could be as large as ~ 2 K similar to the magnitude of what was found during the MY 25 GDS. Using the reanalysis, the life cycle of the planet-encircling global dust storm in MY28 was also studied. The Noachis dust storm that occurred just before the MY 28 GDS was found to be the joint result of a travelling Chryse storm, enhanced by dust lifting along its path and local dust lifting in Noachis itself. The adiabatic heating associated with the north polar warming that occurred during MY 28 GDS was up to ~ 3 times as large as that found during the non-GDS year MY 29. The wind stress dust lifting was shown to in strong correlation with the global average dust loadings, and significantly decreased when the GDS decayed.

### Marshall, S.D. (2014), "Sloping convection: An experimental investigation in a baroclinic annulus With topography"

This thesis documents a collection of experimental investigations in which a differentially-heated annulus was used to investigate the effects of topography on the atmospheric and oceanic circulation. To this end a number of experiments were devised, each using a different topographic base to study a different aspect of the impact of topography, motivated by the most notable outstanding questions found in a review of the literature, namely exploring the effects of topographic resonance, blocking via partial barriers, and azimuthally differential-heating via thermal topography.

First of all, whilst employing sinusoidal wavenumber-3 topography to extend the experimental parameter space of a similar study, namely Read and Risch (2011), a new regime within a region of structural vacillation was encountered. Denoted as the 'stationary-transition' regime, it featured periodic oscillations between a dominant stationary wavenumber-3 flow and axisymmetric or chaotic flow. An investigation into topography resonance followed, keeping the wavenumebr-3 base, but with a sloped lid to add a beta effect to the annulus. This acted to increase the occurrence of stationary waves, along with the 'stationary-transition' regime, which was discovered to be a near-resonant region where nonlinear topography resonant instability led to a 23 to 42 'day' oscillatory structure. The base was then replaced with an isolated ridge, forming a partial barrier to study the difference between blocked and unblocked flow. The topography was found to impact the circulation at a level much higher than its own peak, causing a unique flow structure when the drifting flow and the topography interacted in the form of an 'interference' regime at low Taylor Numbers, as well as forming an erratic 'irregular' regime at higher Taylor Numbers. Lastly, this isolated ridge was replaced by flat heating elements covering the same azimuthal extent, in order to observeewhether thermal topography could be comparable to mechanical topography. These azimuthally-varying heating experiments produced much the same results as the partial barriers study, despite the lack of a physical peak or bottom-trapped waves, suggesting that blocking is independent of these activities. Evidence of resonant wave-triads was noted in all experiments, though the component wavenumbers of the wave-triads and their impact on the flow was found to depend on the topography in question.

### Wang, Y. (2014), "Comparative planetary circulation regimes in simple general circulation models"

This thesis presents the studies of terrestrial planetary atmospheric circulation regimes using simplified GCMs with different levels of complexity. Two different versions of the simplified GCM PUMA (Portable University Model for the Atmosphere) are used - PUMA-S with Newtonian cooling scheme and PUMA-G with a semi-grey two-band radiative transfer scheme and dry convective adjustment. A series of controlled experiments are conducted by varying planetary rotation rate and imposed equator-to-pole temperature difference using PUMAS-S, and by varying rotation rate, planetary obliquity, and the ratio of optical depth in long-wave (thermal radiation) band to that in short-wave (stellar radiation) band using PUMA-G. These defining parameters are further combined with each other into dimensionless forms to establish parameter spaces, in which the occurences of different circulation regimes are mapped and classified. For the PUMA-S experiments, very coherent trends when varying planetary rotation rate (thermal Rossby number) is found. It is demonstrated that the GRW mechanism is mainly responsible for the equato- rial super-rotation observed in our experiments. Regular baroclinic waves are obtained at intermediate values of thermal Rossby number and depend strongly on the strength of radiative and frictional damping. Global atmospheric ener- getics in terms of Lorenz energy cycle and meridional heat transport efficiency also exhibits strong dependence on planetary rotation rate from our PUMA-S experiments. Theories of geostrophic turbulence (especially the recently introduced zonostrophic turbulence) and jet formation are examined using the PUMA-S experiments. For the PUMA-G experiments, Similar trends are observed with respect to varying planetary rotation rate, while new regimes like strongly subrotating atmospheres are found when varying obliquity in PUMA- G. Tidally-locked planets are also studied by modifying the incoming stellar irradiation in PUMA-G. It is found that atmospheric optical depth in the longwave band plays an important role in setting the heat transport efficiency from day-side to night-side. These results provide significant insights into the terrestrial planetary atmospheric circulation dynamics and the inference of circulation regimes of extrasolar planets. Future studies will focus on the effect of seasonal/diurnal cycle, the parametrisation of eddy heat transport efficiency, as well as the modification of the two-band semi-grey radiative transfer scheme to incorporate pressure broadening effects.

### Arnold, H.M. (2013), "Stochastic Parametrisation and Model Uncertainty"

Representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and stochastic parametrisation schemes have been proposed for this purpose. Such schemes have been shown to improve the skill of ensemble forecasts, resulting in a growing use of stochastic parametrisation schemes in numerical weather predic- tion. However, little research has explicitly tested the ability of stochastic parametrisations to represent model uncertainty, since the presence of other sources of forecast uncertainty has complicated the results.

This study seeks to provide firm foundations for the use of stochastic parametrisation schemes as a representation of model uncertainty in numerical weather prediction models. Idealised experiments are carried out in the Lorenz ‘96 (L96) simplified model of the atmo- sphere, in which all sources of uncertainty apart from model uncertainty can be removed. Stochastic parametrisations are found to be a skilful way of representing model uncertainty in weather forecasts in this system. Stochastic schemes which have a realistic representa- tion of model error produce reliable forecasts, improving on the deterministic and the more “traditional” perturbed parameter schemes tested.

The potential of using stochastic parametrisations for simulating the climate is considered, an area in which there has been little research. A significant improvement is observed when stochastic parametrisation schemes are used to represent model uncertainty in climate sim- ulations in the L96 system. This improvement is particularly pronounced when considering the regime behaviour of the L96 system — the stochastic forecast models are significantly more skilful than using a deterministic perturbed parameter ensemble to represent model un- certainty. The reliability of a model at forecasting the weather is found to be linked to that model’s ability to simulate the climate, providing some support for the seamless prediction paradigm.

The lessons learned in the L96 system are then used to test and develop stochastic and perturbed parameter representations of model uncertainty for use in an operational numerical weather prediction model, the Integrated Forecasting System (IFS). A particular focus is on improving the representation of model uncertainty in the convection parametrisation scheme. Perturbed parameter schemes are tested, which improve on the operational stochastic scheme in some regards, but are not as skilful as a new generalised version of the stochastic scheme. The proposed stochastic scheme has a potentially more realistic representation of model error than the operational scheme, and improves the reliability of the forecasts.

While studying the L96 system, it was found that there is a need for a proper score which is particularly sensitive to forecast reliability. A suitable score is proposed and tested, before being used for verification of the forecasts made in the IFS.

This study demonstrates the power of using stochastic over perturbed parameter repres- entations of model uncertainty in weather and climate simulations. It is hoped that these results motivate further research into physically-based stochastic parametrisation schemes, as well as triggering the development of stochastic Earth-system models for probabilistic climate prediction.

### Mendonça, J. (2013), "Studies of Venus using a comprehensive General Circulation Model"

The profusion of observational data made available by the Venus Express and previous space missions, increases our need to develop numerical tools to interpret the data and improve our understanding of the Venus meteorology. The main objective of this work is to develop an improved Venus general circulation model and to study the most likely mechanisms driving the atmosphere to the current observed circulation. Our new model is an extension of a simplified version and includes a new radiative transfer scheme and convection and an adapted boundary layer scheme and dynamical core that take into account the dependence of the heat capacity with temperature, at constant atmospheric pressure. The new radiative transfer formulation implemented is more suitable for Venus climate studies than previous works due to its easy adaptability to different atmospheric conditions. This flexibility of the model was very important in this work to explore the uncertainties on the lower atmospheric conditions such as the gas absorption and the possible presence of aerosols near the surface. The new general circulation model obtains, after long periods of integration, a super-rotation phenomenon in the cloud region quantitatively similar to the one observed. However, this phenomenon is sensitive to some radiative parameters such as the amount of the solar radiative energy absorbed by the surface and the amount of clouds. The super-rotation in the model is formed due to the combined influence of the zonal mean circulation, thermal tides and transient waves, and the main mechanisms involved are identified and studied. In this process the momentum transported by the semidiurnal tide excited in the upper clouds has a key contribution. These migrating waves transport prograde momentum mainly from the upper atmosphere to the cloud region. In this work we also explored the model parameters to gain a better understanding of the effect of topography, the diurnal cycle and convective momentum mixing. In general the results showed that: the topography seemed capable of sustaining stronger global super-rotation; without diurnal cycle the strong winds in the cloud region are not produced; the convective momentum mixing experiment did not lead to significant changes. A simple experiment done advecting the UV absorber in the atmosphere, qualitatively showed several atmospheric phenomena that are important for the distribution of clouds. Among them is the presence of a region of low permeability isolating the polar vortex. This last experiment also showed that when increasing the amount of UV absorption in the upper cloud region the winds get stronger. Following the interpretation of observational data using numerical models, we also used a simplified version of the general circulation model to assess the accuracy of zonal wind retrievals from measured temperatures using the cyclostrophic thermal wind equation in the Venus mesosphere. From this analysis we suggest a method which better estimates the lower boundary condition, and improves the consistency of the results at high latitudes when compared with cloud tracking measurements.

### Jacoby, T.N.L. (2012), "Inertia-gravity wave generation by boundary layer instabilities"

Waves with periods shorter than the inertial period exist in the atmosphere (as inertia-gravity

waves) and in the oceans (as Poincar´e 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 necessitated

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 balance

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 Holmboe,

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 Navier-Stokes model of the rotating thermal annulus. The model predicts

the generation of short waves from ‘wavemaker’ regions determined by strong

shear and downwelling near the inner cylinder. These then propagate into the geostrophic

interior of the fluid as inertia-gravity waves, where they have been detected

in previous laboratory experiments. We then show how these wavemakers are consistent

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.

### Mulholland, D.P. (2012), "Martian dust lifting, transport and associated processes"

The dust lifting capacity of the UK Mars General Circulation Model has been extended

through the development of a new wind stress lifting parameterisation, and the simulation of

a ﬁnite, variable surface dust layer. This second addition, which was represented by the use

of lifting thresholds that were adjusted at each surface gridpoint in response to the removal

or deposition of dust, led to enhanced variability in the timing and peak magnitude of major

dust storms produced in the model. These dust storms were realistic in many respects, and

the observed global dust storm frequency of occurrence of roughly one in every three years

was approximately reproduced by the model, but an artiﬁcial threshold decrease rate was

required to maintain dust lifting on a multiannual timescale — this was believed to be due

to inaccuracies in the net cross-equatorial dust ﬂux, which showed a strong bias towards

the northern hemisphere. Signiﬁcant changes were seen in model dust lifting rates when

the inﬂuence of a heterogeneous surface roughness length was included in the wind stress

scheme, and the need for more sophisticated sub-gridscale methods in future dust lifting

schemes, to cope with this and other eﬀects, was noted. The inclusion of radiatively active

water clouds in model runs also aﬀected dust lifting rates, particularly in the vicinity of

the polar caps in autumn, winter and spring. The dynamics behind the formation of small,

cap-edge dust storms during these periods were examined in detail, and it was found that

a cessation in dust lifting activity that occurs around winter solstice does so due to a

combination of the radiative eﬀects of global dust loading and polar hood ice clouds, and

zonal variations in midlatitude topography. The direct interaction between dust and ice, in

the form of nucleation and scavenging, was investigated. It was found that scavenging by

water ice, if it is suitably eﬃcient, could signiﬁcantly reduce the dust content of the winter

polar regions. However, the dust and ice vertical proﬁles measured in the aphelion cloud

belt by Mars Climate Sounder were not reproduced by the model with any of the possible

scavenging eﬃciencies used. It appears that scavenging cannot provide an explanation for

the existence of sharply deﬁned, elevated dust layers at low latitudes.

### Maddison, J.R. (2011), "Adaptive mesh modelling of the thermally driven annulus"

Numerical simulations of atmospheric and oceanic flows are fundamentally limited by a lack of model resolution. This thesis describes the application of unstructured mesh finite element methods to geophysical fluid dynamics simulations. These methods permit the mesh resolution to be concentrated in regions of relatively increased dynamical importance. Dynamic mesh adaptivity can further be used to maintain an optimised mesh even as the flow develops. Hence unstructured dynamic mesh adaptive methods have the potential to enable efficient simulations of high Reynolds number flows in complex geometries.

In this thesis, the thermally driven rotating annulus is used to test these numerical methods. This system is a classic laboratory scale analogue for large scale geophysical flows. The thermally driven rotating annulus has a long history of experimental and numerical research, and hence it is ideally suited for the validation of new numerical methods.

For geophysical systems there is a leading order balance between the Coriolis and buoyancy accelerations and the pressure gradient acceleration: geostrophic and hydrostatic balance. It is essential that any numerical model for these systems is able to represent these balances accurately. In this thesis a balanced pressure decomposition method is described, whereby the pressure is decomposed into a "balanced" component associated with the Coriolis and buoyancy accelerations, and a "residual" component associated with other forcings and that enforces incompressibility. It is demonstrated that this method can be used to enable a more accurate representation of geostrophic and hydrostatic balance in finite element modelling. Furthermore, when applying dynamic mesh adaptivity, there is a further potential for imbalance injection by the mesh optimisation procedure. This issue is tested in the context of shallow-water ocean modelling. For the linearised system on an *f*-plane, and with a steady balance permitting numerical discretisation, an interpolant is formulated that guarantees that a steady and balanced state remains steady and in balance after interpolation onto an arbitrary target mesh.

The application of unstructured dynamic mesh adaptive methods to the thermally driven rotating annulus is presented. Fixed structured mesh finite element simulations are conducted, and compared against a finite difference model and against experiment. Further dynamic mesh adaptive simulations are then conducted, and compared against the structured mesh simulations. These tests are used to identify weaknesses in the application of dynamic mesh adaptivity to geophysical systems. The simulations are extended to a more challenging system: the thermally driven rotating annulus at high Taylor number and with sloping base and lid topography. Analysis of the high Taylor number simulations reveals a direct energy transfer from the eddies to the mean flow, confirming the results of previous experimental work.

### Young, R.M.B. (2009), "Predictability of a laboratory analogue for planetary atmospheres"

The thermally-driven rotating annulus is a laboratory experiment used to study the dynamics of planetary atmospheres under controlled and reproducible conditions. The predictability of this experiment is studied by applying the same principles used to predict the atmosphere. A forecasting system for the annulus is built using the analysis correction method for data assimilation and the breeding method for ensemble generation. The results show that a range of ﬂow regimes with varying complexity can be accurately assimilated, predicted, and studied in this experiment. This framework is also intended to demonstrate a proof-of-concept: that the annulus could be used as a testbed for meteorological techniques under laboratory conditions.

First, a regime diagram is created using numerical simulations in order to select points in parameter space to forecast, and a new chaotic ﬂow regime is discovered within it. The two components of the framework are then used as standalone algorithms to measure predictability in the perfect model scenario and to demonstrate data assimilation. With a perfect model, regular ﬂow regimes are found to be predictable until the end of the forecasts, and chaotic regimes are predictable over hundreds of seconds. There is a diﬀerence in the way predictability is lost between low-order chaotic regimes and high-order chaos. Analysis correction is shown to be accurate in both regular and chaotic regimes, with residual velocity errors about 3–8 times the observational error. Speciﬁc assimilation scenarios studied include information propagation from data-rich to data-poor areas, assimilation of vortex shedding observations, and assimilation over regime and rotation rate transitions.

The full framework is used to predict regular and chaotic ﬂow, verifying the forecasts against laboratory data. The steady wave forecasts perform well, and are predictable until the end of the available data. The amplitude and structural vacillation forecasts lose quality and skill by a combination of wave drift and wavenumber transition. Amplitude vacillation is predictable up to several hundred seconds ahead, and structural vacillation is predictable for a few hundred seconds.

Zuchowski, L.C. (2009), "Modelling Jupiter's meridional circulations, cloud bands, and moist convective storms"

### Aguiar, A. (2008), "Instabilities of a shear layer in a barotropic rotating fluid"

Above a critical value of horizontal stress, the ﬂow within a bounded system in rotation is driven to an unstable limit, beyond which it develops chains of vortices. The number of these vortices depends not only upon the value of the stress imposed but also on the sense of the shear in some conﬁgurations, highlighting discrepancies between earlier experiments. Quasi-geostrophic theory, however, predicts that there should be no qualitative diﬀerences with respect to the sign of the forcing.

We have studied barotropic instability in laboratory experiments with ﬂat cylindrical geometry, where a detached shear layer occurs tangent to diﬀerentially rotating sections. These sections can either be two discs placed at the top and bottom of the tank or a single thick disc immersed in the ﬂuid. When a single thick disc is used, we observe that the azimuthal wavenumber depends on the sign of diﬀerential rotation.

With axisymmetric numerical simulations, we were able to study the differences in the meridional circulation for different conﬁgurations and sign of forcing. When two discs are used, the circulation occurs in pairs of counter-rotating cells of similar size, if the forcing is weak. For strong and positive forcing only, centrifugal instability sets in. When a single disc is used, one of the circulation cells is typically much stronger than the other and the ﬂow is strongly asymmetric in radius.

The inﬂuence of a topographic β-effect was also investigated in laboratory experiments, using four distinct sloping bottom combinations with the setup of the two discs. In the conﬁgurations studied, unstable modes of shear instability can be stabilised by topography, depending on the combination of sgn(β) with the sign of forcing.

Finally, we studied a possible example of barotropic instability in planetary atmospheres and propose that long-lived polygonal jets such as Saturn’s north polar hexagon should be interpreted as a ﬁnite-amplitude, nonlinear equilibration of a barotropic instability of Saturn’s zonal jet.

### Castrejón-Pita, A.A. (2008), "Synchronization in baroclinic systems"

In recent years, the study of synchronization phenomena in nonlinear systems has made a number of significant advances in various areas of physics, engineering and the life sciences. Ideas of chaos synchronization have been used recently in some atmospheric phenomena as an attempt to better understand certain kinds of cyclic behaviour and teleconnection patterns, and at least some have shown promising results.

This thesis begins with an experimental investigation of baroclinic waves in air in a differentially heated rotating annulus. Air has a Prandtl number of 0.707, which falls within a previously unexplored region of parameter space for experimental baroclinic instability studies. The flow regimes encountered include steady waves, periodic amplitude vacillations, modulated amplitude vacillations and weak waves, the latter characterized by having amplitudes less than 5% of the applied temperature contrast. The distribution of these flow regimes in parameter space is presented in a regime diagram with Taylor numbers ranging from Ta≈1.410^{5} up to Ta≈1.310^{6} and thermal Rossby numbers from Ro≈0.02 up to Ro≈13. It was found that the progression of transitions between different regimes was, as predicted by recent numerical modelling results, from steady to amplitude vacillation regimes, the opposite of what is usually found in experiments with high Prandtl number liquids.

We then moved on to the investigation of the synchronization phenomena using a pair of 5-Dimensional versions of a two-layer quasigeostrophic model of baroclinic instability that had been modified in order to obtain a system coupled through its zonal flows. Unidirectional and bidirectional coupling in both periodic and chaotic regimes were investigated in detail. Various degrees of synchronization including partial, phase, imperfect, generalized and chaos-destroying synchronization were found. In the bidirectional configuration, also oscillation quenching was found.

Finally, an experimental investigation of synchronized thermally driven baroclinic systems was carried out. This configuration placed two such convection experiments on the same rotating turntable and allowed them to be coupled via their thermal control systems. By this means, dynamically-induced variations in the horizontal heat transport within one experimental system (due to vacillations in the amplitude of the baroclinic wave) led to fluctuations in the temperature of coolant fed to the second system. This configuration, just like in the first part of the numerical model is called *master-slave*. Thus, the dynamics of the first system affected in real time the thermal boundary conditions presented to the second system, whilst both systems were maintained on average at similar (though not identical) points in parameter space. The amplitude of these fluctuations were on the order of 1.510^{-3}C (for comparison, the vacillations in the amplitude of the baroclinic wave were of ≈0.4^{}C, yet imperfect and full phase synchronization was found in the periodic regime, whilst only imperfect synchronization was detected in the chaotic regime.

### Wordsworth, R.D. (2008), "Theoretical and experimental investigations of turbulent jet formation in planetary fluid dynamics"

This thesis describes theoretical and experimental investigations of planetary-scale turbulence and jet formation.

In the ﬁrst section, the interaction between zonal jets and planetary waves is described using techniques adapted from quantum mechanics. The planetary waveﬁeld is treated as a ensemble of wavepackets, and the quantum mechanical Wigner function is used to construct an equation for the evolution of wavepacket density in phase space that includes all eﬀects of the mean ﬂow on the waves. Analytical arguments, combined with a simple numerical model, are then used to give an intuitive picture of jet formation as a positive feedback process in which a jet ‘feeds’ on wavepackets as it grows. Furthermore, it is shown that the phase space approach also allows a very intuitive explanation of east-west jet asymmetry in terms of wavepacket motion.

In the second section, a diﬀerentially heated rotating annulus experiment is used to study planetary-scale turbulence and jet formation in the laboratory. The cases of both ﬂat and sloping vertical boundaries were investigated; in the former, it was found that the ﬂow evolved into a statistically steady state typically consisting of a large-scale coherent structure plus a more rapidly varying eddy ﬁeld. In the latter case, the sloping boundaries caused turbulent eddies to behave like planetary waves at large scales, and eddy interaction with the zonal ﬂow then led to the formation of several alternating jets at mid-depth. The jets in the experiment did not scale with the Rhines length, and spectral analysis of the ﬂow indicated a distinct separation between jets and eddies in wavenumber space, with direct energy transfer occuring nonlocally between them. This result suggests that the traditional turbulent cascade picture of zonal jet formation may be an inappropriate one in the geophysically important case of large-scale ﬂows forced by diﬀerential solar heating.

Additional experiments were performed with an insulating barrier that blocked ﬂow in the azimuthal direction. At low rotation rates, a large gyre was observed at mid-depth in the annulus, with an intense ‘southward’ boundary current on the left side of the barrier. At high rotation rates, the ﬂow became turbulent, and the gyre split into several zonal jets away from the barrier. These experiments may have implications for physical oceanography, as recent observations and simulations of the Earth’s deep oceans have indicated that zonal jet formation may also be occurring there.

In the ﬁnal section, the numerical model of the ﬁrst section is extended, in order to produce a simple reduced model of the jet formation observed in the unblocked experiments. The model results were qualitatively very similar to the experiment, although quantitative diﬀerences existed. The reasons for the discrepancies are discussed, along with suggestions for future research and implications for the modelling of real planetary-scale ﬂuids. In particular, it is noted that if nonlocal energy transfer dominates in real geophysical ﬂuids such as the Earth’s atmosphere, it may be possible to construct faster general circulation models that parameterise the eﬀects of eddy-eddy interactions.

### Lee, C. (2006), "Modelling of the Atmosphere of Venus"

A General Circulation Model of the atmosphere of the planet Venus is developed using a climate model developed by the UK Meteorological Ofﬁce. The model is adapted to use a 5◦ × 5◦ horizontal resolution covering the entire horizontal domain with 33 levels extending from the surface to 90km altitude, with a maximum vertical spacing of 3km. Modiﬁcations are made to provide a regime appropriate to the atmosphere of Venus. The rotation and orbital periods are changed to the measured values for Venus, and a realistic temperature proﬁle is used to provide a suitable equilibrium temperature. Radiative and frictional forcing schemes are linearized and adapted to provide a plausible climate while keeping the parameterizations as simple as possible.

A super–rotating atmosphere is found in the simplest model conﬁguration with no diurnal or seasonal cycles, with horizontal equatorward transport of momentum, at altitudes between 40km and 80km, as the mechanism which maintains the equatorial super–rotation. Equatorial Kelvin waves with a period of 9.5 ± 0.5 days and Mixed–Rossby–gravity (MRG) waves with periods of 30 ± 2 days are spontaneously produced in the same model, and the MRG modes are found to contribute signiﬁcantly to the maintenance of

the equatorial super–rotation. The sensitivity of the model to changes in the forcing parameterization is tested and the presence of the equatorial super–rotation is found to be a stable feature for a range of values. The polar region of the model qualitatively reproduces the observed ‘cold collar’ surrounding the middle atmosphere pole, and the ‘warm pole’ in the upper atmosphere.

A passive tracer scheme is implemented in the model and is used to investigate the effect of the atmospheric circulation on simple clouds in the atmosphere. Precipitation, evaporation, and condensation are implemented to provide a source and sink for the volatile tracer. Large scale structures are found in the cloud, similar to the “Y” shape and reversed ‘C’ shape features observed in the atmosphere of Venus. Depletion of the cloud phase of the volatile is seen in the polar regions of the model, is a result of the downwelling in the upper branch of the meridional circulation.

A Monin–Obukhov boundary layer parameterization is integrated into the model and the effect of topography is tested using realistic topography of Venus. No signiﬁcant differences are found in the large scale circulation or magnitude or form of the equatorial super–rotation. However, the surface temperature and pressure are both negatively correlated with topographic height, leading to cold mountains and warm valleys, as would be expected for an optically thick atmosphere.

An idealised diurnal cycle is included in the thermal relaxation ﬁeld to examine the response of the model to a time–varying heating. The diurnal and semi–diurnal tides are found in the circulation and temperature ﬁelds of the model atmosphere, with the tides contributing to the equatorward momentum transport, maintaining an equatorial super-rotation in the model and producing a larger global super–rotation than in the model with zonally symmetric forcing.

Perez, E.P. (2006) "Heat Transport by Baroclinic Eddies: Evaluating Eddy Paramaterizations for Numerical Models"

### Keane, R.J. (2005) "Characterising Lagrangian Stirring in a Thermally Driven Rotating Annulus Flow"

The Lagrangian stirring properties of a ﬂuid held within thermally driven, corotating coaxial cylinders, are characterised numerically using a range of Eulerian and Lagrangian diagnostics. This class of ﬂuid ﬂows is of geophysical interest and can be studied in detail in the laboratory. Three Lagrangian diagnostics for stirring are investigated: a box-counting fractal dimension meausure, a ﬁnite time Lyapunov exponent and a ﬁnite scale Lyapunov exponent. The last two of these have been widely used for characterising the stirring properties of geophysical ﬂows, although the ﬁnite scale Lyapunov exponent is rather recent. The Eulerian diagnostics that are investigated measure departure from ﬂow symmetries, which constrain tracer trajectories to two dimensional phase space. In regions where the ﬂow departs strongly from such symmetries, chaotic trajectories are possible, whereas chaotic trajectories cannot occur if there is no departure from the symmetries; the Eulerian diagnostics therefore provide a possible measure of the stirring properties which does not require explicit integration of tracer trajectories.

Lagrangian tracer trajectories are calculated by integrating the velocity ﬁeld with respect to time, using a second order Runge-Kutta integration and cubic interpolation in space and linear interpolation in time. Two distinct sub-classes of ﬂow are studied: axisymmetric ﬂow with time dependent forcing and steady non-axisymmetric ﬂow. The velocity ﬁeld of both sub-classes deﬁnes a dynamical system with three dimensional phase space, so that the presence of one symmetry is sufﬁcient to constrain tracers to integrable trajectories.

It is found that the ﬁnite time Lyapunov exponent and the ﬁnite scale Lyapunov exponent both characterise the stirring properties effectively; the ﬁnite scale Lyapunov exponent is rather more efﬁcient and reliable. The Eulerian symmetry measures do not identify many of the most distinctive stirring characteristics of the ﬂows, although they do identify some of the large scale stirring properties. Averaged Eulerian symmetry measures are found to correlate strongly with averaged ﬁnite scale Lyapunov exponents, for a range of different ﬂows and planes within ﬂows. The averaged Eulerian symmetry measure can thus provide a reliable measure of the Lagrangian stirring properties of a given ﬂuid ﬂow as a whole, or of a plane within a ﬂow.

Eccles, F.J.R. (2003) "A Laboratory and Numerical Study of Periodically Forced, Nonlinear, Baroclinic Systems"

Böttger, H.M. (2003) "Modelling the Water Cycle on Mars"

### Williams, P.D. (2003) "Nonlinear Interactions of Fast and Slow Modes in Rotating, Stratified Fluid Flows"

This thesis is available for download from the Oxford University Research Archive.

This thesis describes a combined model and laboratory investigation of the generation and mutual interactions of fluid waves whose characteristic scales differ by an order of magnitude or more. The principal aims are to study how waves on one scale can generate waves on another, much shorter scale, and to examine the subsequent nonlinear feedback of the short waves on the long waves. The underlying motive is to better understand such interactions in rotating, stratified, planetary fluids such as atmospheres and oceans. The first part of the thesis describes a laboratory investigation using a rotating, two-layer annulus, forced by imposing a shear across the interface between the layers. A method is developed for making measurements of the two-dimensional interface height field which are very highly-resolved both in space and time. The system's linear normal modes fall into two distinct classes: 'slow' waves which are relatively long in wavelength and intrinsic period, and 'fast' waves which are much shorter and more quickly-evolving. Experiments are performed to categorize the flow at a wide range of points in the system's parameter space. At very small background rotation rates, the interface is completely devoid of waves of both types. At higher rates, fast modes only are generated, and are shown to be consistent with the Kelvin-Helmholtz instability mechanism based on a critical Richardson number. At rotation rates which are higher still, baroclinic instability gives rise to the onset of slow modes, with subsequent localized generation of fast modes superimposed in the troughs of the slow waves. In order to examine the generation mechanism of these coexisting fast modes, and to assess the extent of their impact upon the evolution of the slow modes, a quasi-geostrophic numerical model of the laboratory annulus is developed in the second part of the thesis. Fast modes are filtered out of the model by construction, as the phase space trajectory is confined to the slow manifold, but the slow wave dynamics is accurately captured. Model velocity fields are used to diagnose a number of fast wave radiation indicators. In contrast to the case of isolated fast waves, the Richardson number is a poor indicator of the generation of the coexisting fast waves that are observed in the laboratory, and so it is inferred that these are not Kelvin-Helmholtz waves. The best indicator is one associated with the spontaneous emission of inertia-gravity waves, a generalization of geostrophic adjustment radiation. A comparison is carried out between the equilibrated wavenumbers, phase speeds and amplitudes of slow waves in the laboratory (which coexist with fast modes), and slow waves in the model (which exist alone). There are significant differences between these wave properties, but it is shown that these discrepancies can be attributed to uncertainties in fluid properties, and to model approximations apart from the neglect of fast modes. The impact of the fast modes on the slow modes is therefore sufficiently small to evade illumination by this method of inquiry. As a stronger test of the interaction, a stochastic parameterization of the inertia-gravity waves is included in the model. Consistent with the laboratory/model intercomparison, the parameterized fast waves generally have only a small impact upon the slow waves. However, sufficiently close to a transition curve between two different slow modes in the system's parameter space, it is shown that the fast modes can exert a dominant influence. In particular, the fast modes can force spontaneous transitions from one slow mode to another, due to the phenomenon of stochastic resonance. This finding should be of interest to the meteorological and climate modelling communities, because of its potential to affect model reliability.