|Problems with the energy budget of the Earth - constraints from geodesy and geomagnetism.|
University of California at Los Angeles
|Recent results from Portable Seismic Array Experiments in Peru and Mexico and the Role of Water in Lithospheric Dynamics|
Victoria University of Wellington
|Time-varying seismic anisotropy on Japanese volcanoes|
UC San Diego
|Limitations of earthquake triggering models|
|テレスコープアレイによる最高エネルギー宇宙線の研究 - ユタの砂漠で宇宙線|
Technion - Israel Institute of Technology
|Gravity currents as a test case: do simple mathematical models produce good physical insights, or do good insights generate powerful models?|
King Abdullah University of Science and Technology
|The 2009 Earthquake Crisis and Dike Intrusion in Western Saudi Arabia|
University of California
|Earthquake Forecasting: Should we Base it on Activation, Quiescence, or Something Else?|
Prof. Jacobo Bielak
Carnegie Mellon University
|End-to-end earthquake simulation: from source to urban impact|
Dr. Thorsten W Becker
Department of Earth Sciences, University of Southern California
|Seismological constraints on mantle dynamics|
A gravity current appears when fluid of one density, propagates into another fluid of a different density, 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. Gravity currents 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, etc. A gravity current which propagates inside a stratified fluid (about the neutral buoyancy lever rather than along a boundary) is called ``intrusion''; an important application is the spreading in the atmosphere of umbrella clouds generated by volcanic eruptions (Sukuzi and Koyaguchi, 2009).
Simple qualitative consideration and observations indicate that the gravity current is a very complex, 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. On the other hand, there are mathematical models based on a long line of assumptions such as hydrostatic pressure, sharp interface, Boussinesq system, thin layer, idealized release conditions (see Ungarish, 2009). This enables us to determine the behavior of the averaged variables entirely from theoretical considerations and solutions of ``mathematical models'' which are significantly simpler than the full set of governing equations (the Navier-Stokes system).
The lecture gives a brief presentation of some typical models and solutions. We see that: (a) Qualitatively, the 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 within a few percent, sometimes within the range of the experimental errors. The fact that such simple models give useful results merits attention: is the predictive power of the model a consequence of postulated mathematical simplicity, or is it rather a result of well-selected physical components? Some tentative answers to this universally relevant question, as provided by the test-case of gravity currents and intrusions, are discussed.