BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Nonlinear Waves
SUMMARY:Dynamics of singularities and wavebreaking in 2D h
ydrodynamics with a free surface - Prof Pavel Lush
nikov\, University of New Mexico
DTSTART;TZID=Europe/London:20170608T150000
DTEND;TZID=Europe/London:20170608T160000
UID:TALK72971AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72971
DESCRIPTION:2D hydrodynamics of ideal fluid with a free surfac
e is considered. A\ntime-dependent conformal trans
formation is used which maps a free\nfluid surface
into the real line with fluid domain mapped into
the\nlower complex half-plane. The fluid dynamics
is fully characterized\nby the complex singulariti
es in the upper complex half-plane of the\nconform
al map and the complex velocity. The initially fla
t surface\nwith the pole in the complex velocity t
urns over arbitrary small\ntime into the branch cu
t connecting two square root branch points.\nWitho
ut gravity one of these branch points approaches t
he fluid\nsurface with the approximate exponential
law corresponding to the\nformation of the fluid
jet. The addition of gravity results in\nwavebreak
ing in the form of plunging of the jet into the wa
ter\nsurface. The use of the additional conformal
transformation to\nresolve the dynamics near branc
h points allows analyzing\nwavebreaking in details
. The formation of multiple Crapper capillary\nsol
utions is observed during overturning of the wave
contributing to\nthe turbulence of surface wave. A
nother possible way for the\nwavebreaking is the s
low increase of Stokes wave amplitude through\nnon
linear interactions until the limiting Stokes wave
forms with\nsubsequent wavebreaking. For non-limi
ting Stokes wave the only\nsingularity in the phys
ical sheet of Riemann surface is the\nsquare-root
branch point located. The corresponding branch cut
\ndefines the second sheet of the Riemann surface
if one crosses the\nbranch cut. The infinite numbe
r of pairs of square root\nsingularities is found
corresponding to an infinite number of\nnon-physic
al sheets of Riemann surface. Each pair belongs to
its own\nnon-physical sheet of Riemann surface. A
n increase of the steepness of\nthe Stokes wave me
ans that all these singularities simultaneously\na
pproach the real line from different sheets of Rie
mann surface and\nmerge forming 2/3 power-law sin
gularity of the limiting\nStokes wave. It is conje
ctured that non-limiting Stokes wave at the\nleadi
ng order consists of the infinite product of neste
d square root\nsingularities which form the infini
te number of sheets of Riemann\nsurface. The conje
cture is also supported by high precision\nsimulat
ions\, where a quad (32 digits) and a variable pre
cision (up\nto 200 digits) were used to reliably r
ecover the structure of square\nroot branch cuts i
n multiple sheets of Riemann surface.\n
LOCATION:MR11\, CMS
CONTACT:Prof Natalia Berloff
END:VEVENT
END:VCALENDAR