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SUMMARY:Scattering of water waves by multiple rows of vertical thin barrie
 rs - Jin Huang (University of Bristol)
DTSTART:20230526T124000Z
DTEND:20230526T132500Z
UID:TALK198949@talks.cam.ac.uk
DESCRIPTION:The reflection and transmission of surface waves by a doubly-p
 eriodic array of thin fixed identical vertical barriers extending uniforml
 y through the depth of the fluid is considered. The water wave problem\, w
 hich also has analogues in acoustics and electromagnetics\, involves scatt
 ering by a large finite number of equally spaced rows each consisting of a
  linear periodic array of barriers. The main purpose of the work is to com
 pare the results of two approximate methods of solution based on homogenis
 ation techniques with exact results allowing us to determine when the resu
 lts can be expected to be in good agreement. &nbsp\;When no approximation 
 is made\, a method of solution describing the propagation of incident wave
 s through the exact barrier arrangement is derived using Floquet-Bloch eig
 ensolutions for the corresponding infinite periodic array. &nbsp\;It is sh
 own how the solution can be reduced to a simple pair of integral equations
  which results only from matching the region containing barrier arrays to 
 the two exterior domains. Numerical solutions are\, nevertheless\, relativ
 ely complicated and two approximate models are developed which considerabl
 y simplify the numerical effort required. In one approximation it is assum
 ed only that the spacing between two adjacent rows of barriers is small an
 d is complementary to the commonly-used wide-spacing approximation. The co
 mplication of the geometry is removed by replacing the governing equations
  and boundary conditions with an effective continuous medium and a simplif
 ied pair of integral equations now govern the solutions. In a second conti
 nuum model\, a low-frequency homogenisation approach based on a long-wave 
 assumption is invoked and matching now leads to closed-form expressions fo
 r the reflection and transmission coefficients. Results concentrate on the
  comparison between different methods which allows us to assess the validi
 ty of each continuum model. This understanding will be important in develo
 ping approximate models that describe the operation of wave energy farms c
 onsisting of large arrays of oscillating flaps designed to absorb energy.\
 nThe lecture is based on joint works with Richard Porter.
LOCATION:Seminar Room 1\, Newton Institute
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