Publication: Generation of gravity waves in an experimental facility
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Publication date
2019-06
Defense date
2019-07-05
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Abstract
The development of a computational tool to study the propagation of gravity waves in
water is carried out by reproducing the conditions of an experimental study. The problem
consists in the propagation of a gravity wave in a channel with a bottom topography
where the is already a mean flow in the opposite direction. The physics of such problem
is analogous to the one involved in the Hawking radiation of a black hole, which stresses
the practical importance of the computational tool being developed, given that black holes
are phenomena difficult for us to study.
The problem will be analyzed with both a theoretical and a numerical approach. The
numerical simulations will be performed by means of the software Gerris.
As a first approach, a simpler version of the problem in which the channel is straight
is analyzed. From the theoretical point of view, in these conditions and under some assumptions
about the nature of the flow, the equations describing the motion of the fluid
(Navier-Stokes equations) can be simplified up to a linear theory which provides an analytical
solution. The analytical linear results are then contrasted with those obtained with
a numerical simulation in order to check the validity of the latter. Once this step is accomplished,
the actual problem of a flow in channel with a bottom topography will be studied
by means of a numerical simulation, using the same computational methodology. The
results obtained will be compared to those obtained in the experimental study mentioned
earlier. The aim of this project is to implement a numerical tool that allows us to investigate
up to which point the experimental analogy between gravity waves propagating
against a flume in a channel of variable depth and the Hawking radiation of a black hole
is applicable. The computational tool we will derive can be later extended to the study of
the propagation of water gravity waves in flows under different conditions.
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Keywords
Water gravity wave, Dispersion relation, Froude number, Topography, Numerical simulation, Computational tool, Gerris