Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains xiii, 131 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 129-130).

Call number: LD2668 .T4 1966 M311 / Master of Science

Digitized by Kansas Correctional Industries

Thesis--Ph. D., University of Hong Kong.

No description available.

Cette thèse étudie la formation et l'évolution des jets et des vortexdans les atmosphères planétaires turbulentes, à l'aide d'une doubleapproche de simulations numériques et d'expériences delaboratoire. Pour l'approche numérique, un modèle en fluidesshallow-water quasi-géostrophique à deux couches dans le plan betaavec des conditions canal a été utilisé. Comme dans Panetta (1988), onimplémente un cisaillement vertical pour représenter le gradientlatitudinal de température moyenné spatialement, qui est partiellementmaintenu par un forçage thermique. Les instabilités baroclinesaffaiblissent le gradient de température, alors que le forçagethermique le restaure, ce qui crée une dynamique non-linéaire trèsriche.Tout d'abord, nous avons considéré l'écoulement sur un fond plat, etavons modélisé les mouvements convectifs par des paires decyclones/anticyclones ou `hetons' comme dans Thomson (2016). Nousobtenons ainsi des jets principalement baroclines, oscillants entredes phases calmes et des phases turbulentes, où l'écoulement perd sazonalité. Des vortex se forment à partir des jets méandreux etl'énergie zonale diminue alors que l'énergie tourbillonnaireaugmente. Ces phases turbulentes durent typiquement pendant unepériode de relaxation du forçage thermique. On étudie les effets ducisaillement vertical, du forçage thermique et des hetons, enregardant les transferts d'énergie entre les énergies cinétiques etpotentielles, leurs composantes barotropes et baroclines ainsi queleurs composantes zonales et tourbillonnaires. Ceci nous amène àrepenser le paradigme classique des transferts d'énergie présenté dansSalmon (1982). De plus, nous étudions comment une analyse de stabilitélinéaire de l'écoulement zonal instantané est reliée aux phases calmeset turbulentes.Ensuite, nous considérons l'effet d'une topographie de grande échelle,comme une première approche pour comprendre le rôle de la topographiedans la formation des jets et des vortex. Nous utilisons le mêmemodèle que dans la première étude mais nous ajoutons un fondtopographique linéaire méridionalement, qui a l'avantage de dépendred'un seul paramètre, la pente. Une pente négative approfondit lacouche inférieure par rapport à un fond plat, ce qui augmente lepotentiel des instabilités baroclines, alors qu'une pente positive aun effet stabilisateur. Nous supprimons le forçage par les hetons etperturbons l'écoulement grâce à une zone de Rossby de faibleamplitude dans la couche inférieure à l'instant initial. L'effetprincipal du forçage par les hetons est d'agir comme une sorted'amortissement : les fluctuations de l'énergie sont constamment plusextrêmes que sans forçage. Une analyse de stabilité linéaire esteffectuée afin de déterminer les zones de stabilité etd'instabilité.Pour l'étude expérimentale, nous utilisons une cuve tournanteremplie par deux couches de fluides avec une stratification au sel etun couvercle rigide en rotation différentielle. Nous étudions unfront barocliniquement instable dans le régime des vacillationsd'amplitude, qui est caractérisé par l'émergence et ladisparition de vortex de grande échelle. L'analyse de deuxexpériences à la limite de la géostrophie, avec des nombres deRossby de Ro=0.4 et Ro=0.6, montre des comportement trèsdifférents. Pour un faible nombre de Rossby, nous observons desdipôles baroclines alors que pour un large nombre de Rossby nousobtenons des vortex barotropes. Nous examinons l'activité des ondesde petite échelle par différentes méthodes qui révèlent laprésence d'ondes d'inertie gravité comme précurseures del'émergence des vortex.Afin de poursuivre nos recherches sur les fronts à l'interface entredeux couches de fluides immiscibles, nous avons développé unenouvelle méthode de détection de la hauteur et de la pente baséesur les lois optiques de la réfraction. Les équations théoriquesassociées sont résolues numériquement et validées à l'aidede plusieurs situations idéalisées. / This thesis investigates the formation and evolution of jets andvortices in turbulent planetary atmospheres using a dual approach ofhigh-resolution numerical simulations and novel laboratoryexperiments. A two-layer quasi-geostrophic beta-channel shallow watermodel is used for the numerical study. As in Panetta (1988), avertical shear is implemented to represent a spatially-meanlatitudinal temperature gradient, which is partially maintained bythermal damping. Baroclinic instabilities work to erode thetemperature gradient, while thermal damping acts to restore it. Asthe basic state vertical shear is unstable, the thermal damping cannotlead to a full recovery, thus modifying subsequent instabilities andleading to rich nonlinear dynamical behaviour.First, we consider flow over a flat bottom, and model convectivemotions like those thought to occur on Jupiter by pairs ofcyclones/anti-cyclones or `hetons' as in Thomson (2016). We therebyobtain predominantly baroclinic jets, oscillating between quiescentphases, when jets are zonal and the energy is nearly stationary, andturbulent phases, when the flow loses its zonality, vortices pinch offfrom the meandering jets, and zonal energy components drop while eddyenergy components increase. These turbulent phases typically last fora thermal damping relaxation period. The impacts of vertical shear(baroclinicity), thermal damping and heton forcing are comprehensivelyinvestigated by considering the energy transfers occurring betweenkinetic and potential energy, their barotropic and baroclinic parts aswell as their zonal and eddy parts. This leads to a rethinking of theclassic paradigm of energy transfer presented by Salmon (1982), asthis paradigm is too simplistic to explain the results found.Then, we consider the effect of large-scale bottom topography, as afirst approach to understanding the role of topography in jet andvortex formation. We use the same model as in the first study butinclude a linearly sloping topography which has the advantage of beingcharacterised by a single parameter, the slope. We omit the hetonforcing and instead perturb the flow with a small amplitude Rossbywave initially. The main effect of heton forcing is actually to act asa kind of damping: energy fluctuations are consistently less extremethan when no forcing is used. A linear stability analysis is carriedout to motivate a series of nonlinear simulations investigating theeffect of topography, in particular, differences from the flat bottomcase previously examined. We find that destabilising topography makesthe jets more dynamic.In the experimental part, a two-layer salt-stratified fluid is used ina rotating tank with a differentially rotating lid to generate theshear across the interface. We consider a baroclinically unstablefront in the regime of amplitude vacillation, which is found to becharacterised by the sequential emergence and disappearance of alarge-scale vortex. Analysing two similar experiments at the limit ofgeostrophy, with different Rossby numbers Ro=0.4 and Ro=0.6, showssurprisingly different behaviours, with a baroclinic dipole for small,and a barotropic vortex for the large Rossby number. The small-scalewave activity is explored using different methods, and the resultssuggest small, spontaneously-arising inertia-gravity waves precedingthe emergence of the vortex which stirs the interface, thus having animpact on the mixing between the two layers. The recovery period ofthe amplitude vacillation, as well as the intensity of the vortex,increases with the Rossby number.For further research on fronts at two-layer immiscible interfaces, avery accurate novel optical method has been developed to detect theheight and slope, based on the refractive laws of optics. Theassociated theoretical equations are solved numerically and validatedin various idealised situations.

The effect of rotation on the stability of multiple jets in planetary atmospheres is system- atically investigated. Typically in Jovian planetary atmospheres, multiple zonal jets have been observed and their morphology has been systematically studied. The formation of jets has always been viewed as a nonlinear problem where most work has followed from the ideas of potential vorticity (PV) homogenization or turbulent mixing on a β-plane. In our present work, we have aimed to look at the linear stability of multiple jets in a geophysical fluid, and hope to add further insight into the observed jet profiles in β-plane turbulence. In addition, we also study the evolution and life-cycle of these jets as they interact with each other in a non linear fashion. We begin with the linear stability of the \Bickley jet" using the linearized shallow water quasigeostrophic (QG) equations. We have included a finite deformation radius in our calculations to partially mimic the effects of compressibility. A family of synthetically generated velocity profiles with east-west jets are then studied. In particular, a variety of flow configurations with two jets have been considered with a parameter sweep across jet separation, relative jet strength and thickness. As a broad observation, it is noted that an asymmetric east-west jet profile with a stronger and sharper eastward jet is the most stable of all the profiles considered, and a finite deformation radius further stabilizes such profiles. More realistic jet profiles have also been considered and the role of a finite deformation radius in stabilizing such jets is elucidated. We also examined the nonlinear evolution of multiple jets in a periodic domain and in a channel geometry, as we undertake freely decaying long time simulations of the governing QG equation. As per the \Selective Decay" principle we observe that arbitrary initial conditions approach the flow configuration of the prescribed \suitable end states". In addition, we have shown how a finite deformation length scale modifies these \suitable end states". As a broad observation, we have noted that a linearly unstable jet flow configuration, in the presence of β, breaks down into turbulence and reforms into a more asymmetric jet profile with a stronger and sharper eastward jet. The inclusion of a finite deformation length scale in our calculations, is observed to suppress such jet formation. Similar numerical experiments have been performed in a channel and the results have been compared. Chiefly, for the end states, the nature of the observed jet asymmetry is reversed, i.e., the westward jets are observed to be stronger in a channel.

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy