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)
Abstract: A 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.
Date: Monday, 29 October, 2pm, (QUEENS 1.04)
Speaker: Prof Grae Worster (University of Cambridge)
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)
Abstract: The 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 . 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  and the semi-classical theories based on the WKB approximation, extended to the case with complex eigen-energy.
 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
 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.
Date: Monday, 12 November, 2pm, (MED 1.02)
Speaker: Dr Helen Burgess (University of St. Andrews)
Date: Monday, 19 November, 2pm, (QUEENS 0.08)
Speaker: Prof Kostas Bellibasakis (National Technical University of Athens)
Date: Monday, 26 November, 2pm, (ZICER 0.02)
Speaker: Dr David Lloyd (University of Surrey)
Date: Monday, 10 December, 2pm, (QUEENS 0.08)
Speaker: Dr Giovanni Barontini (University of Birmingham)