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SEMINAR: Internal wave seiching/standing-waves.

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Today's date is Friday, May 07, 2021
Internal wave seiching/standing-waves. : This seminar is part of the Centre for Water Research seminar series. Other events...
There have been many recordings of internal wave spectra in lakes.When the density profile is so that it can be approximated by a few (often two) layers of constant density there has been satisfactory agreement between the observed spectra and calculated seiche frequencies.

The situation with continuous stratification is less satisfactory.There have been several careful laboratory studies of exactly periodic standing waves in containers. Uniform stratification, constant buoyancy frequency, is the most common setup reported. There is a good picture of standing waves in a trapezoidal tank in a paper in Nature: http://www.nature.com/nature/journal/v388/n6642/abs/388557a0.html. (There have been many later experiments with similar pictures.)

Standing waves as above may be modelled with a stream function satisfying the one-dimensional wave equation - in space variables - equation (9.11.6) of Imberger 'Environmental Fluid Dynamics'. Boundary conditions for a closed container have the stream function constant around the boundary. The problem is mathematically not well set. Eigenspaces are infinite dimensional.

It is possible to suggest a dichotomy with two sorts of standing wave/seiche motions. On the one hand there are very smooth seiche-style oscillations as familiar with the classical solutions in rectangular boxes, semicircles, etc On the other hand there is internal wave "focusing" - with its clear evidence of the characteristic directions. See the picture in the Nature paper.

My work suggests that this dichotomy shouldn't be over-stated. Even in the nice domains with the smooth solutions there are plenty of solutions clearly showing the characteristics.The mathematics involved in this main conclusion is extremely simple.


Grant's first degree is from UWA - in Applied Maths.Grant first met Jorg early in 1968 when Jorg was researching for his MSc at UWA,and he was tutoring, marking time before semester started in Cambridge. Grant's PhD was on "waves and free-streamline flows" at the Department of Applied Maths and Theoretical Physics at Cambridge. After a couple of postdocs, Grant joined the staff of UWA's Maths Department in 1974, and worked there until the end of 2010. His research has involved various fluid dynamics problems,those of greatest relevance to CWR being surface water waves and internal waves.He has had a range of other interests, partly driven by who would fund his research leaves in England.

Grant has some sessional teaching in Engineering Maths at Curtin University, and some non-CWR research there. A CV and publication list is up at https://sites.google.com/site/keadyperthunis/home

Grant lives close to UWA, and has family/carer responsibilities requiring him to be able to get home more easily than is possible from Curtin. The career change from Maths to CWR is proving slower than anticipated.The work described in today's talk was motivated by a CWR concern with mixing at shorelines associated with internal wave behaviour there, and more generally that seiche frequencies are detectable in measured internal wave spectra.

It is too theoretical to be of immediately applicable, but may be of longer term relevance to scientific understanding of mixing. After getting this one submitted Grant is determined to change to computations - seiching frequencies, SWAN, etc. - concentrating on comparing theoretical results with those from computer codes.And, Grant truly loves math. software - Mathematica and Maple and Matlab -and likes helping people with these.

PS* This seminar is free and open to the public & no RSVP required.

****All Welcome****
Speaker(s) Grant Keady, Maths Department, Curtin University, and CWR Visitor.
Location Blakers Lecture Room, Ground Floor, Mathematics Building, The University of Western Australia
Contact Askale Abebe <[email protected]> : 6488 7565
URL https://sites.google.com/site/keadyperthunis/home
Start Wed, 13 Nov 2013 16:00
End Wed, 13 Nov 2013 17:00
Submitted by Askale Abebe <[email protected]>
Last Updated Fri, 07 Feb 2014 12:40
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