Determination of the bottom deformation from space- and time-resolved water wave measurements

• Autores: Cobelli, Pablo Javier; Petitjeans, Philippe; Maurel, Agnès; Pagneux, Vincent
• Año de publicación: 2017
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Surface Gravity Waves; Waves/Free-Surface Flows
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In this paper we study both theoretically and experimentally the inverse problem of indirectly measuring the shape of a localized bottom deformation with a non-instantaneous time evolution, from either an instantaneous global state (space-based inversion) or a local time-history record (time-based inversion) of the free-surface evolution. Firstly, the mathematical inversion problem is explicitly defined and uniqueness of its solution is established. We then show that this problem is ill-posed in the sense of Hadamard, rendering its solution unstable. In order to overcome this difficulty, we introduce a regularization scheme as well as a strategy for choosing the optimal value of the associated regularization parameter. We then conduct a series of laboratory experiments in which an axisymmetric three-dimensional bottom deformation of controlled shape and time evolution is imposed on a layer of water of constant depth, initially at rest. The detailed evolution of the air–liquid interface is measured by means of a free-surface profilometry technique providing space- and time-resolved data. Based on these experimental data and employing our regularization scheme, we are able to show that it is indeed possible to reconstruct the seabed profile responsible for the linear free-surface dynamics either by space- or time-based inversions. Furthermore, we discuss the different relative advantages of each type of reconstruction, their associated errors and the limitations of the inverse determination.
Fil: Cobelli, Pablo Javier. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Petitjeans, Philippe. Paristech; Francia
Fil: Maurel, Agnès. Institut Langevin Ondes Et Images; Francia
Fil: Pagneux, Vincent. Laboratoire D'acoustique de L'universite Du Maine; Francia