We will present results from studies of the impact of the non-slow (typically fast) components of a rotating, stratified flow on its slow dynamics. We 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 Ma- jda [1996] and others.

In order to understand how the flow approaches and interacts with the slow dynamics we decompose the full solution, where u is a vector of all the unknowns, as

u = u α + u ′α where α represents the Ro → 0, F r → 0 or the simultaneous limit of both (QG for

quasi-geostrophy), with

P α u α = u α    P α u ′α = 0 ,

and where Pαu represents the projection of the full solution onto the null space of the fast operator. We use this decomposition to find evolution equations for the components of the flow (and the corresponding energy) on and off the slow manifold.

Numerical simulations indicate that for the geometry considered (triply periodic) and the type of forcing applied, the fast waves act as a conduit, moving energy onto the slow manifold. This decomposition clarifies how the energy is exchanged when either the stratification or the rotation is weak. In the quasi-geostrophic limit the energetics are less clear, however it is observed that the energy off the slow manifold equilibrates to a quasi-steady value.

We 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? We will give an example for the quasi-geostrophic limit of the Boussinesq equations.

At the end we will briefly discuss how understanding the role of oscillations has allowed us to develop convergent algorithms for parallel-in-time methods.

Beth A. Wingate - University of Exeter

Jared Whitehead - Brigham Young University

Terry Haut - Los Alamos National Laboratory

Most sensing systems exhibit so-called ‘sidelobe’ responses, which can be interpreted as an inevitable effect in one domain of truncation of the signal in the Fourier-complement domain.  Perhaps the best-known example is in antenna theory where sidelobes are an inevitable consequence of the fact that the antenna aperture must be finite.  The effect also appears in many other places, for example in time-frequency conversions and in the range domain of a pulse-compressed radar which radiates a signal only over a finite frequency band.  In the range domain these sidelobes extend over twice the length of the transmitted pulse.  For a conventional radar with relatively short pulses the effect of these unwanted returns is thus confined to a relatively short part of the range swathe.

Some of the most modern radar techniques, however, use continuous, noise-like transmissions.  ‘Primary’ noise-modulated radars are in their infancy but so-called ‘Passive’ radars using broadcast transmissions as their power source receive similar signals.  The sidelobes of even a small target at very short range can be larger than the main return from a target at much greater range.  This limits the dynamic range of the radar.

Since, however, the sidelobe pattern is predictable if the illuminating signal is known sufficiently accurately, the expected sidelobes due to a large target can be estimated and removed to tidy up the image.  This approach was first described formally in:

Hoegbom, J. A., ‘Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines,’ Astrom. Astrophys. Suppl. 15, pp417-26, 1974.

And is generally known by the name of the ‘CLEAN’ algorithm.

The seminar will outline the problem, outline the basic form of the algorithm and ask questions about what is possible with non-iterative versions of the algorithms, how to process the data coherently and how to understand any stability issues associated with the algorithm.

Details: 

1) Shape optimization of a paddle for density-viscosity measurements in oilfield environment;

2) Phenomenology of Kapitza thermal resistance with coupling at the MD to macroscopic scale.

Abstract:

(i) We consider the modelling of freezing of fluids which contain particulates and fibres (imagine orange juice “with bits”) flowing in channels. The objective is to design optimum geometry/temperatures to accelerate freezing.

(ii) We present the challenge of setting-up a model for lithium or sodium ion stationary energy storage cells and battery packs to calculate the gravimetric and volumetric energy density of the cells and cost. Depending upon the materials, electrode content, porosity, packing electrolyte and current collectors. There is a model existing for automotive called Batpac.