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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Whitham modulation theory and water waves - Thomas
Bridges (University of Surrey)
DTSTART;TZID=Europe/London:20220711T100000
DTEND;TZID=Europe/London:20220711T110000
UID:TALK175823AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175823
DESCRIPTION:Whitham modulation theory (WMT) has had an impact
on the theory of water waves since the beginning o
f the subject in the early 1960s. This talk will f
ocus on three topics of current interest. The firs
t is ocean wave forecasting\, where the "fundament
al law for wave prediction" is the conservation of
wave action. This theory is reviewed and generali
sations to finite amplitude discussed\, including
how coalescing characteristics in WMT arise in wav
e forecasting. The second problem is the transitio
n point of the Benjamin-Feir instability which occ
urs in relatively shallow water. The Whitham (1967
) modulation equations for this problem are review
ed\, new properties discussed\, and re-modulation
is introduced at the transition point to find a di
spersive higher-order modulation equation due to R
atliff (2017). This latter equation contains wave
jumps and frequency shifting. The third topic is h
ow WMT illuminates defects in shallow water hydrod
ynamics\, where Stokes waves of differing amplitud
e and wavenumber are joined by a shock. Sprenger &
Hoefer (2020) use WMT to construct these shocks i
n the fifth-order KdV equation. This latter theory
is reviewed\, and implications and generalisation
s discussed.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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