Oceanographic Implications of Wave-Induced Turbulent Diffusion
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Laboratory and theoretical models of planetary-scale instabilities and waves
Research work is proceeding in theoretical, numerical, and experimental geophysical fluid dynamics leading up to a reflight of the GFFC (Geophysical Fluid Flow Cell Experiment) on USML-2. The work is intended not only to generate ideas for future space experiments, but to provide fundamental results concerned with nonlinear and chaotic properties of thermal convection and baroclinic waves in terrestrial and planetary atmospheres. The major efforts are focussed on thermal convection in a rapidly rotating annulus relevant to Jovian atmospheric dynamics, and on the chaotic behavior of baroclinic waves relevant to the Earth's atmosphere. The approach, in preparation for USML-2, is primarily theoretical and numerical. Mechanistic process models are solved numerically in order to identify physical mechanisms that may be observed in the GFFC, and which are important in real geophysical applications. The results from numerical simulations of geophysical fluid flow (subject to rotation and stratification) are compared with previous GFFC experiments on Spacelab-3 and with existing and proposed terrestrial laboratory experiments of various types. Pattern recognition algorithms have been employed to generate low-dimensional descriptions of the highly nonlinear and turbulent numerical simulations. Such empirically truncated descriptions provide for simplified but robust physical interpretations of the dynamics, as well as yielding highly efficient computations of these chaotic flows.
Hart, John E.↗
Statistical Analysis of the Limiting Dynamics of Two dimensional Boussinesq Turbulent Systems
In the current study, we investigate rotational and stratified turbulent systems within the framework of the Boussinesq equations. The effects of rotation and stratification give rise to a variety of dynamical regimes in atmospheric and oceanic turbulence. To develop a better understanding of the fundamental flow properties through a more straightforward mathematical framework, we commence our research with a simplified two-dimensional Boussinesq model that incorporates rotation and stratification effects. We explore two distinct limiting dynamics, considering pure rotation and pure stratification separately. We examine these intriguing dynamics through numerical investigations, applying the exact solution theory of Boussinesq equations and examining small-scale perturbations to the exact solution under rotation and stratification. We conduct an analysis of statistical quantities associated with the turbulent state variables. The results indicate that, under weak rotation at the equilibrium statistical state, the flow field exhibits vortex flow. However, strong rotation transforms the flow into vertical shear flow. We observe both downscale and upscale energy transfers with a decay rate of k −3 in the absence of external forcing and dissipation. Furthermore, we delve into the study of internal gravity wave mode interactions in the simplified two-dimensional Boussinesq system, which is a crucial aspect of geophysical turbulence due to gravity. Our findings reveal that the time series of the mode coefficients exhibit wave-like interactions between wave modes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Theoretical and experimental studies in support of the geophysical fluid flow experiment
Meteorologists and astrophysicists interested in large scale planetary and solar circulations have come to recognize the importance of rotation and stratification in determining the character of these flows. In particular, the effect of latitude-dependent Coriolis force on nonlinear convection is thought to play a crucial role in such phenomena as differential rotation on the Sun, cloud band orientation on Jupiter, and the generation of magnetic fields in thermally driven dynamos. The continuous low-gravity environment of the orbiting space shuttle offers a unique opportunity to make laboratory studies of such large-scale thermally driven flows under the constraint imposed by rotation and sphericity. This is possible because polarization forces in a dielectric liquid, which are linearly dependent on fluid temperature, give rise to an effectively radial buoyancy force when a radial electrostatic field is imposed. The Geophysical Fluid Flow Cell (GFFC) is an implementation of this ideal in which fluid is contained between two rotating hemispheres that are differentially heated and stressed with a large a-c voltage. The experiment, to be flown on Spacelab III (currently set for launch April 29, 1985), will explore non-linear mode selection and high Rayleigh number turbulence in a rotating convecting spherical shell of liquid. Experiments will be carried out in a low driving parameter range where some limited numerical experimentation is currently feasible, as well as in a parameter range significantly beyond numerical computation for many years.
Hart, J.↗