Journal of Fluid Mechanics Webinar Series: UKFN Thesis Competition Winners
- Date
- Friday 27 November 2020, 16.00
- External URL
- https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/fluid-mechanics-webinar-series
- Category
- JFM Webinar Series
Speaker: Hannah Kreczak, University of Newcastle, UK
Date/Time: Friday 27th November, 2020. 4:00 pm GMT/11 am EST
Title: Rates of mixing in models of fluid devices with discontinuities
Abstract: The dynamics of mixing by cutting and shuffling are subtle and not well understood. We present mixing dynamics arising from fundamental models capturing the essence of discontinuous stirring with diffusion. When the stirring is governed by purely cutting and shuffling, we reveal that the time to achieve a mixed condition varies polynomially with diffusivity rate with an exponent less than unity. In stirring fields which are chaotic we observe that the addition of discontinuous transformations contaminates mixing. Long-time mixing rates behave counter-intuitively when varying the diffusivity rate and a deceleration of mixing with increasing diffusion coefficient is observed, sometimes overshooting analytically derived bounds.
Speaker: Peter Baddoo, Imperial College London, UK
Date/Time: Friday 27th November, 2020. 4:20 pm GMT/11:20 am EST
Title: Analytic solutions for flows through cascades
Abstract: Motivated by turbomachinery aeroacoustics, we investigate the flow through a periodic array of disconnected objects, termed a “cascade”. We deploy and develop techniques from complex analysis to elucidate the mathematical structures and physical mechanisms relevant to cascade flows. Our approach considers both aerodynamic and aeroacoustic aspects but we focus efforts toward developing conformal mapping techniques amenable to cascades of complicated geometry and topology. The foundation of practical conformal mapping is the Schwarz–Christoffel (SC) formula; we extend the SC formula to periodic domains which enables analytic constructions of the periodic flow field. By utilising tools from function theory, our solutions are valid for an arbitrary number of obstacles per period window. We also present algorithmic advances that enable rapid and accurate calculations of our mappings. Our theory is applied to classical idealised problems such as steady potential flows, unsteady vortex dynamics, and free-streamline flows. These low-order techniques can be used in turbomachinery design schemes or for real-time flow control with data-driven methods.
Enjoy free access to papers in support of Baddoo's webinar, courtesy of the Journal of Fluid Mechanics.
Speaker: James Steer, University College Dublin, Ireland
Date/Time: Friday 27th November, 2020. 4:40 pm GMT/11:40 am EST
Title: X-Waves and Modulation Instability
Abstract: Modulation instability is characterised by a rapid transfer of energy from a dominant central frequency to sideband frequencies. Dispersive media such as water, optics, and Bose-Einstein condensate, all allow for modulation instability. In the space-time domain, modulation instability manifests itself as a single extreme wave crest arising from an initially periodic, constant amplitude wavetrain. Given the sudden appearance of an unexpectedly high wave crest, the modulation instability has long been proposed as a mechanism by which extreme ocean waves are formed. In this talk I will present the experimental work performed with various collaborators in both the University of Edinburgh’s circular basin (FloWave) and University College London’s combined wave-current flume. In the FloWave basin we observed the propagation of a nondispersive X-wave, a wave structure capable of transporting an extremely large wave at its centre over vast distances without dispersing. The X-wave was predicted using the three-dimensional nonlinear Schrödinger equation (NLSE) to balance nonlinear, dispersive, and diffractive wave properties. At University College London we showed experimentally how a linear vertically sheared current reduces the growth rate of modulation instability as predicted by a modified version of the NLSE, the constant vorticity NLSE (vor-NLSE).