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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dispersive shock waves in coastal flows - Ted John
son (University College London)
DTSTART;TZID=Europe/London:20220712T140000
DTEND;TZID=Europe/London:20220712T143000
UID:TALK175853AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175853
DESCRIPTION:Coastal or boundary currents are an integral part
of global ocean circulation. For example\, current
s may respond to external forcing or intrinsic ins
tability by expelling vortex filaments or larger e
ddies into the ocean\, with implications for the m
ixing of coastal and ocean waters\; and currents d
riven by outflows are important for the transport
of freshwater\, pollutants and land-derived nutrie
nts. There is also much interest in the behaviour
of &lsquo\;free&rsquo\; fronts\, i.e. those that a
re far from the coast\, which can be used to model
western boundary currents such as the Gulf Stream
or the Kuroshio Extension. In the limit of rapid
rotation the governing equations reduce to the qua
si-geostrophic equations - a modified form of the
two-dimensional Euler equations. For the problems
considered here the vorticity of the flow is unity
within the current and zero elsewhere. The unappr
oximated solution can thus be obtained numerically
to high accuracy by applying the method of Contou
r Dynamics to the development of the current-ocean
interface. These solutions provide comparisons fo
r estimating the accuracy of asymptotic solutions.
\nAlongshore variations in the flows take place ov
er scales large compared to offshore scales and so
analysis of the flows leads naturally to a long-w
ave equation for the current- ocean interface. Two
examples will be discussed in depth. First\, the
development of the flow when fluid is discharged f
rom a source on the coast to turn and form an alon
gshore current (Johnson et al. 2017) and\, second\
, the Riemann problem for the subsequent developme
nt of a step change in width of a coastal flow (Ja
mshidi & Johnson 2020).The flux function appearing
in the long-wave equation is non-convex and this
leads to a wide variety of behaviours. Many of the
se are well-described following the method of El (
2005) but some discrepancies remain. These and som
e other open questions will be noted.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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