Applied Mathematics Seminars 

Spring 2015

All seminars (unless otherwise stated) will take place on Tuesdays at 3.00pm in Room 505 in the Mathematics Department (25 Gordon Street). See see how to find us for further details. There will be tea afterwards in Maths Room 606. If you require any more information on the Applied seminars please contact Prof Slava Kurylev e-mail: y.kurylev AT ucl.ac.uk or tel: 020-7679-7896.

13 January 2015

Prof Beth Wingate - University of Exeter

Title: The influence of fast waves and fluctuations on the evolution of slow solutions of the Boussinesq equations

Abstract:
I will present results from studies of the impact of the non-slow (typically fast) components of a rotating, stratified flow on its slow dynamics. My collaborators and I work in the framework of fast singular limits that derives from the work of Bogoliubov and Mitropolsky [1961], Klainerman and Majda [1981], Shochet [1994], Embid and Majda [1996] and others. To understand how the flow approaches and interacts with the slow dynamics we decompose the full solution into its slow component and everything else. We use this decomposition to find evolution equations for the components of the flow (and the corresponding energy) into and out of the 'slow manifold'. Numerical simulations indicate that for the geometry considered (triply periodic) and the type of forcing applied, the fast dynamics act as a conduit, moving energy onto the slow component.

I will also discuss generalizations of the method of cancellations of oscillations of Schochet for two distinct fast time scales, i.e. which fast time scale is fastest? I will give an example for the quasi-geostrophic limit of the Boussinesq equations.

The talk includes joint work with Jared Whitehead (Brigham Young University) and Terry Haut (Los Alamos National Laboratory).

20 January 2015

Prof Alexey Chernov - University of Reading

Title: Quasi-optimal stability estimates for the hp-Raviart-Thomas projection operator on the cube

Abstract:

Stability of the hp-Raviart-Thomas projection operator as a mapping H^1(K) -> H^1(K) on the unit cube K in R^3 has been addressed e.g. in [2], see also [1]. These results are suboptimal w.r.t. the polynomial degree. In this talk we present quasi-optimal stability estimates for the hp-Raviart-Thomas projection operator on the cube. The analysis involves elements of the polynomial approximation theory on an interval and the real method of Banach space interpolation.

(Joint work with Herbert Egger, TU Darmstadt)

[1] Mark Ainsworth and Katia Pinchedez. hp-approximation theory for BDFM and RT finite elements on quadrilaterals. SIAM J. Numer. Anal., 40(6):2047–2068 (electronic) (2003), 2002.

[2] Dominik Schötzau, Christoph Schwab, and Andrea Toselli. Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal., 40(6):2171–2194 (electronic) (2003), 2002.

27 January 2015

Prof Alexander Stegner - Ecole Polytechnique, France

Title: Cyclone-anticyclone asymmetries of island wake flows

Abstract:
A large number of recent studies show that even if the upstream forcing is symmetrical (uniform flow and circular island) the wake flow may exhibit a strong cyclone-anticyclone asymmetry due to the combined effects of rotation and stratification. At mesoscale, laboratory experiments and numerical simulations reveal the preferred formation of anticyclonic vortices within a shallow-water wake if the island diameter is larger than the first baroclinic radius. Once they are formed, these large-scale anticyclones tend to be more stable and robust to external strain perturbations than their cyclonic counterparts. At submesoscale, large scale experiments performed on the Coriolis plateform and 3D numerical simulations have shown that an island wake flow may exhibit a transient and three-dimensional instability in the region of intense anticyclonic vorticity. This instability is a branch of the inertial-centrifugal instability in the framework of rotating,stratified shallow-water flows. In such case, we could expect a predominance of intense cyclone in the island wake.

These various dynamical regimes are mainly controlled by three dimensionless numbers, namely the island Rossby number RoI , the Burger number Bu and the Ekman number Ek. A global diagram, which estimates the various regions of cyclonic or anticyclonic predominance is proposed in the (RoI ; Bu) parameter space.

3 February 2015

Dr Olga Trichtchenko - UCL

Title: Stability of Periodic Gravity-Capillary Water Waves 

Abstract:
I will present results on the computation and stability of periodic surface gravity-capillary waves.  First, I will show how we solve Euler's equations to compute these waves. Then I will present the results of the stability analysis for these solutions by making use of Hill's method. Depending on the coefficient of surface tension, we see resonant effects called Wilton's ripples. These resonant solutions for gravity-capillary waves are found to have interesting instabilities. Since this stability analysis is general to all Hamiltonian systems, we can also use it to compare and contrast the results for different models for water waves.

10 February 2015

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17 February 2015 - NO SEMINAR (READING WEEK)

24 February 2015

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3 March 2015

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10 March 2015 - COLLOQUIUM TALK

Prof Sylvia Serfaty - Université Pierre et Marie Curie

- please see the Departmental Colloquia webpage

17 March 2015

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24 March 2015

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