Louis-Alexandre Couston

Landslide tsunamis in lakes

Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This phenomenon has claimed lives and caused damage to near-shore properties. Landslide tsunamis in lakes are different from typical earthquake tsunamis in the open ocean in that (i) the affected areas are usually within the near-field of the source, (ii) the highest runup occurs within the time period of the geophysical event, and (iii) the enclosed geometry of a lake does not let the tsunami energy escape. To address the problem of transient landslide tsunami runup and to predict the resulting inundation, we utilize a nonlinear model equation in the Lagrangian frame of reference. The motivation for using such a scheme lies in the fact that the runup on an inclined boundary is directly and readily computed in the Lagrangian framework without the need to resort to approximations. In this work, we investigate the inundation patterns due to landslide tsunamis in a lake. We show by numerical computations that Airys approximation of an irrotational theory using Lagrangian coordinates can legitimately predict runup of large amplitude. We also demonstrate that in a lake of finite size the highest runup may be magnified by constructive interference between edge-waves that are trapped along the shore and multiple reflections of outgoing waves from opposite shores, and may occur somewhat later after the first inundation.

Fabry-Perot resonance of water waves.

We show that significant water wave amplification is obtained in a water resonator consisting of two spatially separated patches of small-amplitude sinusoidal corrugations on an otherwise flat seabed. The corrugations reflect the incident waves according to the so-called Bragg reflection mechanism, and the distance between the two sets controls whether the trapped reflected waves experience constructive or destructive interference within the resonator. The resulting amplification or suppression is enhanced with increasing number of ripples and is most effective for specific resonator lengths and at the Bragg frequency, which is determined by the corrugation period. Our analysis draws on the analogous mechanism that occurs between two partially reflecting mirrors in optics, a phenomenon named after its discoverers Charles Fabry and Alfred Perot.

Bragg Resonance of Gravity Waves and Ocean Renewable Energy

Here we study Bragg resonance of surface and interfacial waves. Specifically, we show one triad resonance between two surface waves and one seabed component in a homogeneous fluid, and another triad between a surface wave, an interfacial wave and a bottom component in a two-layer density stratified fluid. Via the Bragg resonance between two surface waves in a homogeneous fluid we can transfer the energy of one wave to another wave with the same frequency that moves in a different direction. We use this type of Bragg resonance to design lenses and curved mirrors for gravity waves. These lenses and mirrors are merely small changes to the seabed topography (e.g. by placing obstacles) and hence are surface non-invasive. By a concave mirror or a convex lens of gravity waves, we can focus gravity waves at a specific location. This may be of interest to the ocean wave energy, as instead of putting a multitude of wave energy harvesting devices over a large area, one large wave energy absorber can be placed at the focal point. This will reduce the cost, increase the efficiency and is clearly more environmentally friendly. We also show that Bragg resonance of surface and interfacial waves can be used to transfer energy from surface waves to interfacial waves, and from interfacial waves to the surface waves. Therefore in a two-layer density stratified fluid a proper architecture of the topography can be used to create a buffer zone which is protected from surface waves. This idea, known as cloaking, can protect floating offshore wind towers from the momentum of oceanic waves.

Sheltering the Shore via Nearshore Oblique Seabed Bars

Periodic seabed undulations, such as nearshore sandbars, are known to reflect incoming surface waves of twice the wavelength by the so-called Bragg resonance mechanism. In view of this property, longshore seabed-mounted bars were proposed long ago as a means of coastal protection against the high momentum of incident oceanic waves. Many theoretical, computational, experimental and field measurements were conducted to understand their effectiveness in shielding the shore. The idea, nevertheless, proved impractical when Yu and Mei (JFM 2000, [1]) showed that due to an inevitable finite reflection from the shoreline, energy can get trapped in the area between the shoreline and the patch of bars eventually resulting in a much higher wave energy flux impinging the shoreline. Here we propose an arrangement of oblique bars that shelters the shore by diverting, rather than reflecting, shore-normal incident waves to the shore-parallel direction. A protected buffer zone is thus created at the shoreline. We show that this novel arrangement can very efficiently shelter the shore, is almost insensitive to the distance between the bottom corrugations and the shoreline, is relatively robust against frequency detuning, and will discuss that it can be designed to protect the shore against almost the entire broadband spectrum of incident waves.Copyright