The Mathematics of Layers and Interfaces (15w5065)

Arriving in Oaxaca, Mexico Sunday, November 8 and departing Friday November 13, 2015


(University of British Columbia)

Nicholas Brummell (University of California at Santa Cruz)

(University of Cambridge)

(University of California at Santa Cruz)

(University of Alberta)


The various communities that have traditionally studied these questions are usually non-overlapping, being divided between applied mathematics, physical oceanography, geophysics and astrophysics. The applied mathematical methods used to approach the problem include weakly nonlinear theory and pattern formation, focusing on generic behaviors such as the formation of fronts, localized solutions, and coarsening. New developments also involve direct statistical simulations, in which moments of the Naviers Stokes equations are determined instead of running simulations of the full primitive equations. The approaches more often used in physical oceanography include laboratory and field experiments on the applied side, together with mean-field hydrodynamics on the theory side. Geophysical and astrophysical approaches have traditionally used even simpler dimensional analysis, but have recently moved to high-performance numerical modeling and are now leading the subject in this context.

This meeting is the first one of its kind, dedicated to cross-disciplinary but mathematically-oriented understanding of layered systems. A recent meeting on Double-Diffusive Systems in 2012, organized by Pascale Garaud, was held in Santa Cruz (CA) and had some sessions dedicated to thermohaline and thermo-compositional layers in the ocean and in lakes. The Division of Planetary Sciences meeting of the American Astronomical Society, as well as the American Geophysical Union, often host sessions related to planetary atmospheres, and sometimes more specifically on jets. However, no meeting dedicated to the crossover between the fields, and in particular to the mathematical models underlying the description of staircases, has ever been held.

The objectives of this 5-day meeting are:

(A) To bring the various communities that study layers and interfaces in different topics of application, and using different mathematical and numerical techniques, together.
(B) To learn from each-other what mathematical/numerical methods are typically used in a given field to study the various questions (1-3) listed above
(C) To compare approaches, their pros and cons, and determine whether they could be successfully exported to another field of application
(D) To understand the similarities/differences between the various fluid systems considered, and construct new generally applicable mathematical models that capitalize on these finding as appropriate

The first three days of the meeting will host a large number of pedagogical talks to reach objectives A-B. The next two days will have, in addition to the talks, more time for informal group discussions and break-out sessions to discuss questions (1-3) specifically, across disciplines, addressing objectives C-D.