BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Whitham modulation theory and water waves - Thomas Bridges (Univer
 sity of Surrey)
DTSTART:20220711T090000Z
DTEND:20220711T100000Z
UID:TALK175823@talks.cam.ac.uk
DESCRIPTION:Whitham modulation theory (WMT) has had an impact on the theor
 y of water waves since the beginning of the subject in the early 1960s. Th
 is talk will focus on three topics of current interest. The first is ocean
  wave forecasting\, where the "fundamental law for wave prediction" is the
  conservation of wave action. This theory is reviewed and generalisations 
 to finite amplitude discussed\, including how coalescing characteristics i
 n WMT arise in wave forecasting. The second problem is the transition poin
 t of the Benjamin-Feir instability which occurs in relatively shallow wate
 r. The Whitham (1967) modulation equations for this problem are reviewed\,
  new properties discussed\, and re-modulation is introduced at the transit
 ion point to find a dispersive higher-order modulation equation due to Rat
 liff (2017). This latter equation contains wave jumps and frequency shifti
 ng. The third topic is how WMT illuminates defects in shallow water hydrod
 ynamics\, where Stokes waves of differing amplitude and wavenumber are joi
 ned by a shock. Sprenger & Hoefer (2020) use WMT to construct these shocks
  in the fifth-order KdV equation. This latter theory is reviewed\, and imp
 lications and generalisations discussed.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR