On the emergence and evolution of jets and vortices in turbulent planetary atmospheres

Planets--Atmospheres--Statistical methods;Planets--Atmospheres--Mathematical models;Vortex-motion

Jougla, Thibault ; Dritschel, David Gerard ; Dritschel, David Gerard

University:University of St Andrews

Department:Mathematics & Statistics (School of)

关键词: Planets--Atmospheres--Statistical methods;    Planets--Atmospheres--Mathematical models;    Vortex-motion;   

Others  :  https://research-repository.st-andrews.ac.uk/bitstream/handle/10023/17924/ThibaultJouglaPhDThesis.pdf?sequence=2&isAllowed=y

来源: DR-NTU

【 摘 要 】

This thesis investigates the formation and evolution of jets and vortices in turbulent planetary atmospheres using a dual approach of high-resolution numerical simulations andnovel laboratory experiments. A two-layer quasi-geostrophic beta-channel shallow watermodel is used for the numerical study. As in Panetta (1988), a vertical shear is implementedto represent a spatially-mean latitudinal temperature gradient, which is partiallymaintained by thermal relaxation. Baroclinic instabilities work to erode the temperaturegradient, while thermal relaxation acts to restore it. As the basic state vertical shear isunstable, the thermal relaxation cannot lead to a full recovery, thus modifying subsequentinstabilities and leading to rich nonlinear dynamical behaviour.First, we consider flow over a flat bottom, and model convective motions like thosethought to occur on Jupiter by pairs of cyclones/anti-cyclones or ‘hetons’ as in Thomson(2016). We thereby obtain predominantly baroclinic jets, oscillating between quiescentphases, when jets are zonal and the energy is nearly stationary, and turbulent phases,when the flow loses its zonality, vortices pinch off from the meandering jets, and zonalenergy components drop while eddy energy components increase. These turbulent phasestypically last for a thermal relaxation period. The impacts of vertical shear(baroclinicity), thermal relaxation and heton forcing are comprehensively investigatedby considering the energy transfers occurring between kinetic and potential energy, theirbarotropic and baroclinic parts as well as their zonal and eddy parts. This leads to arethinking of the classic paradigm of energy transfer presented by Salmon (1982), as thisparadigm is too simplistic to explain the results found.Then, we consider the effect of large-scale bottom topography, as a first approach tounderstanding the role of topography in jet and vortex formation. We use the same modelas in the first study but include a linearly sloping topography which has the advantageof being characterised by a single parameter, the slope. We omit the heton forcing andinstead perturb the flow with a small amplitude Rossby wave initially. The main effectof heton forcing is actually to act as a kind of damping: energy fluctuations are consistentlyless extreme than when no forcing is used. A linear stability analysis is carriedout to motivate a series of nonlinear simulations investigating the effect of topography,in particular, differences from the flat bottom case previously examined. We find thatdestabilising topography makes the jets more dynamic.In the experimental part, a two-layer salt-stratified fluid is used in a rotating tank with a differentially rotating lid to generate the shear across the interface. We considera baroclinically unstable front in the regime of amplitude vacillation, which is found tobe characterised by the sequential emergence and disappearance of a large-scale vortex.Analysing two similar experiments at the limit of geostrophy, with different Rossby numbersRo=0.4 and Ro=0.6, shows surprisingly different behaviours, with a baroclinic dipolefor small, and a barotropic vortex for the large Rossby number. The small-scale wave activity is explored using different methods, and the results suggest small, spontaneously arising inertia-gravity waves preceding the emergence of the vortex which stirs the interface, thus having an impact on the mixing between the two layers. The recovery period of the amplitude vacillation, as well as the intensity of the vortex, increases with the Rossbynumber.For further research on fronts at two-layer immiscible interfaces, a very accurate noveloptical method has been developed to detect the height and slope, based on the refractivelaws of optics. The associated theoretical equations are solved numerically and validatedin various idealised situations.