Plenary Lecture

The Flow of Gravity Currents and Intrusions: A Test-Case for the Power and Limitations of Simple Mathematical Models in the Prediction of Complex Phenomena

Professor Marius Ungarish
Department of Computer Science
Technion - Israel Institute of Technology
E-mail: unga@cs.technion.ac.il

Abstract: A gravity current appears when fluid of one density, ρc, propagates into another fluid of a different density, ρa, and the motion is mainly in the horizontal direction. A gravity current is formed when we open the door of a heated house and cold air from outside flows over the floor into the less dense warm air inside. A gravity current is formed when we pour honey on a pancake and we let it spread out on its own. A gravity current which propagates inside a stratified fluid (rather than along a boundary) is called “intrusion.” Gravity currents (intrusions) originate in many natural and industrial circumstances and are present in the atmosphere, lakes and oceans as winds, cold or warm streams or currents, polluted discharges, volcanic ash clouds, etc. The efficient understanding and prediction of this phenomenon is important in numerous industrial, geophysical, and environmental circumstances.
Simple qualitative consideration and observations indicate that the gravity current is a very com- plex, multi-faced, and parameter-rich physical manifestation. Nevertheless, the gravity current also turns out to be a modeling-friendly phenomenon. Indeed, visualizations of the real flow field reveal an extremely complicated three-dimensional motion, with an irregular interface, billows, mixing, and instabilities. The accurate numerical simulation of this flow from the full set of governing equations (the Navier-Stokes system) requires weeks of number-crunching on powerful computer arrays. On the other hand, there are “mathematical models” for the gravity current, whose derivation is based on a long line of assumptions such as hydrostatic pressure, sharp interface, Boussinesq system, thin layer, idealized release conditions. This simplified set of equations enables us to determine the behavior of the averaged variables entirely from analytical considerations and/or numerical solutions that require insignificant CPU time.
The lecture gives a brief presentation of some typical models and solutions. We show that: (a) Qualitatively, the simplified theory is able to provide the governing dimensionless parameters and the salient features of the various flow regimes; and (b) Quantitatively, the simple models predict velocities of propagation which agree with experiments and full Navier-Stokes simulations within a few percent, typically within the range of the experimental errors. We argue that the gravity-current analysis can be considered a test-case for the methodology of flow-field modelling: the fact that simple models give useful predictions is a result of well-selected physical components. The implementation of this conclusion in the selection of reliable tools for practical applications is discussed.

Brief Biography of the Speaker: Ungarish is presently George Farkas Professor in the Department of Computer Science at the Technion, Israel Institute of Technology, Haifa. His research is focused on modelling, simulation and interpretation of fluid dynamic problems. He graduated Cum Laude in Aeronautical Engineering at the Technion, and did his DSc at the same institute in Applied Mathematics on the simulation and modelling of rotating fluids. He continued his work on similar problems at MIT in the department of Applied Mathematics as a Rothschild and Bantrell post-doc (with H. P. Greenspan) and lec- turer. He has held numerous visiting positions including at MIT, University of Cambridge DAMTP, Technical University Vienna, Institut Polytechnique de Grenoble, University of Witwatersrand at Johannesburg, University of Florida at Gainesville, and National Taiwan University at Taipei.
Ungarish is an authority in modelling and investigation of motion of complex fluids in the presence of gravity, centrifugal and Coriolis forces. He made fundamental contributions to the understanding, modelling and simulation of spin-up processes (of suspensions, stratified fluids, and magnetohydro- dynamical fluids), the Taylor column effect, and propagation of gravity currents and intrusion, in particular for stratified and non-Boussinesq systems (a topic of high relevance to environmental flows like propagation of pollutants, volcanic ash clouds, oil slicks over the sea surface, and similar phe- nomena). He published numerous research papers on these topics in prestigious journals, contributed the chapter on gravity currents in the recent “Handbook of Environmental Fluid Dynamics” (edited by H. J. Fernando, CRC Press, Taylor and Francis Group, 2012), and wrote two well-received books: “Hydrodynamics of Suspensions: Fundamentals of Centrifugal and Gravity Separation,” Springer- Verlag, 1993; and “An Introduction to Gravity Currents and Intrusions,” CRC Press, Taylor and Francis Group, 2009.

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