Autumn 2018 Seminars and Abstracts Autumn 2018 Seminars and Abstracts

Title: Linear stability and nonlinear dynamics of two-layer flow in the presence of surfactants

Date: Monday, 8 October, 2pm, (SCI 1.20)

Speaker: Dr Anna Kalogirou (UEA)

AbstractA two-fluid shear flow in the presence of surfactants is considered. The flow configuration comprises two superposed layers of viscous and immiscible fluids confined in a long horizontal channel. The two fluids can have in general different densities, viscosities and thicknesses. The surfactants can be insoluble, i.e. located at the interface between the two fluids only, or soluble in the lower fluid. A primary aim of this study is to investigate the effect of surfactants on the stability of the interface, and in particular surfactants in high concentrations and above the critical micelle concentration (cmc). An asymptotic model valid in the approximation of a thin fluid layer is also derived, comprising a set of nonlinear PDEs to describe the evolution of the film thickness and surfactant concentration. Interfacial instabilities are induced due to the acting forces of gravity and inertia, as well as the action of Marangoni forces generated as a result of the dependence of surface tension on the interfacial surfactant concentration. The underlying physical mechanism responsible for the formation of interfacial waves will be discussed, together with the complex flow dynamics (typical nonlinear phenomena associated with thin-film flows include travelling waves, solitary pulses, quasi-periodic and chaotic dynamics).

Title: Dynamically Consistent Parameterization of Mesoscale Eddies

Date: Monday,15 October, 2pm, (JSC 1.02)

Speaker: Dr Pavel Berloff (Imperial College London)

Abstract: This work aims at developing new approach for parameterizing mesoscale eddy effects for use in non-eddy-resolving ocean circulation models. These effects are often modelled as some diffusion process or a stochastic forcing, and the proposed approach is implicitly related to the latter category. The idea is to approximate transient eddy flux divergence in a simple way, to find its actual dynamical footprints by solving a simplified but dynamically relevant problem, and to relate the ensemble of footprints to the large-scale flow properties.

 

Title: (In)stability and evolution of inhomogeneous, broad-banded seas

Date: Monday, 22 October, 2pm, (QUEENS 2.22)

Speaker: Dr Raphael Stuhlmeier (University of Plymouth)

Abstract: Nonlinear interaction, along with wind input and dissipation, is one of the three mechanisms which drive wave evolution, and is included in every modern wave-forecast model. The mechanism behind the nonlinear interaction terms in such models is based on the kinetic equation for wave spectra derived by Hasselmann. This does not allow, for example, for statistically inhomogeneous wave fields, nor for the modulational instability which depends on such inhomogeneity, and which has been implicated in the appearance of exceptionally high rogue waves.

Beginning with the basics of third-order wave theory, we sketch the derivation of a discretized equation for the evolution of random, inhomogeneous surface wave fields on deep water from Zakharov's equation, along lines first laid out by Crawford, Saffman, and Yuen. This allows for a general treatment of the stability and long-time behaviour of broad-banded sea states. It is investigated for the simple case of degenerate four-wave interaction, and the instability of statistically homogeneous states to small inhomogeneous disturbances is demonstrated. Furthermore, the long-time evolution is studied for several cases and shown to lead to a complex spatio-temporal energy distribution. The possible impact of this evolution on the statistics of rogue wave occurrence is explored within the framework of this simplified example.

 

Title: The Dynamics of Marine Ice Sheets

Date: Monday, 29 October, 2pm, (QUEENS 1.04)

Speaker: Prof Grae Worster (University of Cambridge)

Abstract: Most of the West Antarctic Ice Sheet (WAIS) sits on bedrock that is one to two kilometres below sea level. Its weight causes the ice sheet to flow outwards towards the ocean, thinning as it goes until it is thin enough to float on the ocean as an ice shelf before it ultimately breaks up into ice bergs. Some areas of the WAIS have been accelerating in recent years, as the point at which the sheet begins to float recedes, and this contributes to the rise in global sea level. I shall describe some recent analogue laboratory experiments and associated mathematical models that describe and quantify the fundamental dynamical controls on ice sheets that terminate in the ocean, focusing particularly on the role that floating ice shelves play in buttressing the ice sheet against collapse.

 

Title: Stability of a vortex with winding number two of the nonlinear Schrödinger equation for Bose-Einstein condensates

Date: Friday, 2 November, 2pm, (SCI 1.20) [please note change of usual day]

Speaker: Dr Hiromitsu Takeuchi (Osaka City University)

AbstractThe stability of doubly quantized vortex (DQV), a vortex with winding number two, in uniform system is a crucial problem in low temperature physics. If a DQV could be stable, a lot of literatures in the long history of research on superfluid system should be re-examined since they assumed a multiply quantized vortex should be unstable there. In this work, we revisit this fundamental problem of the stability of a DQV in uniform single-component Bose-Einstein condensates at zero temperature [1]. To reveal the stability, the system-size dependence of the excitation frequency of the system with a DQV was analyzed through large-scale simulations of the Bogoliubov-de Gennes equation.

We found that the system remains dynamically unstable even in an infinite-system-size limit. The system-size dependence is characterized by introducing the perturbation theory, based on the theory of Hamiltonian dynamical systems [2] and the semi-classical theories based on the WKB approximation, extended to the case with complex eigen-energy.

[1] Hiromitsu Takeuchi, Michikazu Kobayashi, and Kenichi Kasamatsu, Is a Doubly Quantized Vortex Dynamically Unstable in Uniform

Superfluids?, Journal of the Physical Society of Japan 87, 023601 (2018); arXiv:1710.10810

[2] R. S. MacKay, in Hamiltonian Dynamical Systems, ed. R. S. MacKay and J. D. Meiss (Adam Hilger, Bristol, U.K., 1987) p. 137.

 

Title: Planning ultrasound surgery with 3D patient specific models

Date: Monday, 5 November, 2pm, (QUEENS 2.22)

Speaker: Prof Robin Cleveland (University of Oxford)

Abstract: High intensity focused ultrasound has been used clinically to thermally ablate tissue, for example destroying cancer tumours, and to mechanically fractionating tissue, for example enlargening the urethra in the prostate. In order to focus the ultrasound it is normally assumed that the sound speed in soft-tissue is uniform and so it is mostly limited to targets with soft-tissue paths. In reality tissue has a range of different sound speeds, with fat typically 100 m/s slower than other soft-tissue. This can affect the ability to focus accurately. Here two applications are considered using realistic 3D patient models derived from CT data. The first is thermal ablation of the kidney where it is shown that fat layers in the path can result in fragmentation of the focus. It is shown that if the phase aberration can be accounted for then it is possible to recover a tight focus. In the second application it is shown that be using an array it is possible to focus ultrasound to the centre of a vertebral disc, despite the presence of the bone structures. A paradigm for mechanically fractionating tissue in the disc is described employing cavitation nucleation agents. These examples, demonstrate how patient specific models can be employed to improve the performance of high intensity focused ultrasound.

 

Title: Long frontal waves and dynamic scaling in freely evolving equivalent barotropic flow

Date: Monday, 12 November, 2pm, (MED 1.02)

Speaker: Dr Helen Burgess (University of St. Andrews)

AbstractWe present a scaling theory that links the frequency of long frontal waves to the decay rate of kinetic energy and inverse transfer of potential energy in freely evolving equivalent barotropic turbulence. The flow is initialised with a potential vorticity field whose characteristic length scale is LD, the Rossby radius of deformation. As the turbulence evolves fronts of width O(LD) emerge, bounding large vortices within which potential vorticity is well-mixed and arranged into a staircase structure. The jets collocated with the fronts support long wave undulations with wavelengths >> LD and time scales fast relative to the time scale of the flow evolution. These undulations facilitate collisions and mergers between the vortices, implicating the frontal dynamics in the growth of potential-energy-containing flow features. Mergers generate disturbances with radius of curvature O(LD), which then propagate along the jets, causing them to shed filaments of kinetic energy and smooth out. A decay law for the total frontal length LF(t)~t^(-1/3) follows from assuming self-similar vortex growth and using the dispersion relation for long frontal waves [1]. High resolution simulations show that kinetic energy, potential enstrophy, and enstrophy, which are concentrated along the fronts and proportional to LD*LF(t), decay like t^(-1/3). Interestingly this is the same decay law followed by enstrophy in the vortex populations of freely evolving barotropic turbulence [2, 3].

 

Title: Wave propagation in nearshore/coastal environment by coupled-mode models (problems and applications)

Date: Monday, 19 November, 2pm, (QUEENS 0.08)

Speaker: Prof Kostas Bellibasakis (National Technical University of Athens)

Abstract: Results from the development and application of coupled-mode models to predict propagation of water waves in nearshore/coastal environment with variable bathymetry and other inhomogeneities are presented, including interaction with marine structures. This method models reflection, refraction, diffraction and dispersion phenomena, without introducing mild-slope type assumptions. The theory is based on an improved representation of the field in a series of local vertical modes, enhanced by appropriate terms to satisfy boundary conditions on the free surface and the sloping bottom. The additional modes significantly accelerate the convergence of the modal expansion and make the method suitable for horizontally large-scale applications. Next, with the aid of variational principles, the problem of propagation and interaction in non-homogeneous environment is reformulated as a system of partial differential equations on the horizontal plane, having the property to reduce to mild-slope type models in subregions where bathymetry and other parameters are slowly varying, saving computational cost. Various examples are presented and discussed demonstrating the applicability of the present method, including effects of waves on marine floating or fixed structures in an environment characterized by variable bottom topography.

 

Title: Unstable Interfaces and Plumes

Date: Monday, 19 November, 4pm, (SCI 1.20)

Speaker: Prof Larry Forbes (University of Tasmania, Australia)

Abstract:

In many applications involving waves at the surface of a fluid, it is often sufficient just to consider steady-state situations, where the wave pattern does not change noticeably with time.  Waves behind moving ships are one such example.  There is an enormous literature on such situations, and at least for two-dimensional flow, steady waves can be computed reasonably accurately.

 As computers have developed, it has now become possible to look at 2D and even 3D unsteady problems, where the fluid interface evolves with time.  These unsteady flows have some surprising behaviour, both analytically and numerically.  If fluid viscosity is ignored, it is now known that classical flows such as the Rayleigh-Taylor Instability fail within finite time, when the curvature of the free surface becomes infinite at certain points.  This appears to be a common feature in unsteady inviscid flows.  In other geometries, such as the initially spherical outflow from a source, unsteady effects can lead to the surprising result that the lowest mode is the most unstable, so that a one-sided outflow jet evolves.

 This talk will consider some examples of unsteady fluid flow, characterized by the presence of an unstable interface.  We will discuss how fluid viscosity and interface thickness change the singular behaviour predicted by (non-linear) inviscid theory, in some surprisingly subtle ways.

 

Title: Localised patterns and invasion fronts on the surface of a ferrofluid

Date: Monday, 26 November, 2pm, (ZICER 0.02)

Speaker: Dr David Lloyd (University of Surrey)

AbstractIn this talk, I will give an overview of work (both mathematical and experimental) on localised pattern formation seen on the surface of a magnetisable fluid seen in experiments. I will also present on-going work looking at proving the existence of radial spots and invasion fronts where cellular hexagon spikes are left behind in the wake of the front. 

 

Title: Multi-component Bose-Einstein condensates: from neutron stars to ultracold engines

Date: Monday, 10 December, 2pm, (QUEENS 0.08)

Speaker: Dr Giovanni Barontini (University of Birmingham)

Abstract: I will present our latest results on the thermodynamics of spin-1 polar Bose-Einstein Condensates, including evidence of the observation of 2-photon Feshbach resonances, and our progress towards the realization of a “quantum printer” that will allow us to simulate high-energy physics phenomena. In particular, I will present our recent work aiming at unveiling the Andreev-Bashkin effect in superfluid mixtures. In the final part of the talk I will present the progress of our project for the realization of quantum engines using ultracold atomic mixtures.

For further details about the seminars, or to join our mailing list, please contact Anna Kalogirou. For details of previous talks, please use the menu links on the left.