Theory of Water Waves

Water waves are a dramatic, potentially dangerous, yet beautiful phenomena that is omnipresent and impacts every aspect of life on the planet. At smaller length scales the ripples driven by surface tension affect remote sensing. At intermediate length scales waves in the mid-ocean affect shipping and near the shoreline they control the coastal morphology and the ability to navigate along shore. At larger length scales waves such as tsunamis and hurricane-generated waves can cause devastation on a global scale. Across all length scales an exchange of momentum and thermal energy between ocean and atmosphere occurs affecting the global weather system and the climate.

  • 1 hour
    Boundary element and spectral methods for water waves
    P Guyenne (University of Delaware) Friday 18th July 2014 - 13:00 to 14:00
    29 August 2014, 2:51 pm
  • 59 minutes 23 seconds
    Why bouncing droplets are a pretty good model of quantum mechanics
    Brady, A (University of Cambridge) Tuesday 05 August 2014, 15:00-16:00
    13 August 2014, 3:37 pm
  • 35 minutes 41 seconds
    Transverse instability of generalised solitary waves
    Wahlén, E (Lund University) Tuesday 05 August 2014, 16:30-17:30
    13 August 2014, 3:36 pm
  • 58 minutes 3 seconds
    Changing forms and sudden smooth transitions of tsunami waves
    In some tsunami waves travelling over the ocean, such as the one approaching the eastern coast of Japan in 2011, the sea surface of the ocean is depressed by a small meter-scale displacement over a multi-kilometer horizontal length scale, lying in front of a positive elevation of comparable magnitude and length, which together constitute a "down-up" or ``breather'' wave. Shallow water theory shows that the latter travels faster than the former and, according to the extended Korteweg-de Vries model presented here, the waves undergo a transition. Firstly, the two parts coincide at a given position and time producing a maximum elevation, whose amplitude depends on the shape of the approaching wave. Typically this amplitude is larger than the initial displacement magnitude by a factor which can be as large as two, which may explain anomalous elevations of tsunamis at particular positions along their trajectories. It is physically significant that for these small amplitude waves, no wave breaking occurs and there is no excess dissipation. Secondly, following the transition, the elevation wave moves ahead of the depression wave and the distance between them increases either linearly or logarithmically with time.The implications for how these ``down-up'' tsunami waves reach beaches are considered. This is joint work with Chow & Hunt.
    13 August 2014, 3:35 pm
  • 58 minutes 16 seconds
    Hydrodynamic Surface Wave Analogues for Quantum Mechanics and Nonlinear Optics
    Milewski, P (University of Bath) Thursday 31 July 2014, 16:30-17:30
    6 August 2014, 3:49 pm
  • 1 hour 6 minutes
    Global bifurcation for steady gravity water waves with constant vorticity and critical layers
    Varvaruca, E (University of Reading) Thursday 31 July 2014, 15:00-16:00
    5 August 2014, 12:18 pm
  • 58 minutes 18 seconds
    Ill-posedness of truncated series models for water waves
    Some numerical methods for water waves, such as the Craig-Sulem method, involve expanding terms in the water wave evolution equations as series, truncating those series, and then simulating the resulting equations. For one such scheme, we present analytical evidence that the truncated system is in fact ill-posed; this involves further reducing the evolution equations to a model for which we can prove ill-posedness. We then present numerical evidence that the full truncated system is ill-posed, showing that arbitrarily small data can lead to arbitrarily fast growth. We present this numerical evidence for multiple levels of truncation. We are able to prove that by adding a viscosity to the system, we instead arrive at a well-posed initial value problem. This is joint work with Jerry Bona and David Nicholls.
    5 August 2014, 12:16 pm
  • 39 minutes 41 seconds
    Coastal Wave Modelling: General Engineering Usage and Areas for Improved Research
    Bunn, N (HR Wallingford) Wednesday 30 July 2014, 14:40-15:10
    1 August 2014, 12:33 pm
  • 34 minutes 45 seconds
    100-year and 10,000-year Extreme Significant Wave Heights - How Sure Can We Be of These Figures?
    Rainey, R; Colman, J (Atkins Oil & Gas) Wednesday 30 July 2014, 16:00-16:30
    1 August 2014, 12:31 pm
  • 34 minutes 58 seconds
    Numerical Simulation of Wave Loads on Static Offshore Structures
    Jasak, H; Gatin, I; Vukcevic, V (Wikki Ltd) Wednesday 30 July 2014, 15:30-16:00
    1 August 2014, 12:29 pm
  • 36 minutes 21 seconds
    Ocean Wave Measurements: The Challenges and Consequences for the Wave Energy Industry
    Doherty, K (Aquamarine Power) Wednesday 30 July 2014, 14:10-14:40
    1 August 2014, 12:27 pm
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