Raphael Stuhlmeier

ON EDGE WAVES IN STRATIFIED WATER ALONG A SLOPING BEACH

Building on previous investigations, we show that Gerstners famous deep water wave and the related edge wave propagating along a sloping beach, found within the context of water of constant density, can both be adapted to provide explicit free surface flows in incompressible fluids with arbitrary density stratification.

Internal Gerstner waves: applications to dead water

We give an explicit solution describing internal waves with a still-water surface, a situation akin to the well-known dead-water phenomenon, on the basis of the Gerstner wave solution to the Euler equations.

ON CONSTANT VORTICITY FLOWS BENEATH TWO-DIMENSIONAL SURFACE SOLITARY WAVES

We demonstrate that, for a two-dimensional, steady, solitary wave profile, a flow of constant vorticity beneath the wave must likewise be steady and two-dimensional, and the vorticity will point in the direction orthogonal to that of wave propagation. Constant vorticity is the hallmark of a harmonic velocity field, and the simplified vorticity equation is used along with maximum principles to derive the results.

WEC Design Based on Refined Mean Annual Energy Production for the Israeli Mediterranean Coast

Using the Israeli Mediterranean as an example, we address the impact of resource variability and device survivability on the design of floating-body wave-energy converters (WECs). Employing a simplified heaving-cylinder as a prototypical WEC, several device sizes, corresponding to the most frequently encountered and most energetic sea-states in the Israeli Mediterranean, are investigated. Mean-annual energy production is calculated based on the scatter-diagram/power-matrix approach. Subsequently, a measure for significant device motions under irregular sea-states akin to the spectral significant wave-height is developed, and cut-offs to regular operation are explored from the perspective of these significant displacements. The impact of this WEC down-time is captured in a refinement of mean-annual energy production, which consists of supplementing the scatter-diagram/power-matrix calculations by a Boolean displacement matrix. In the Israeli Mediterranean, where most of the annual incident wave power comes in infrequent winter storms, larger WECs outperform smaller WECs by a greater margin when down-time is taken into account. Analogous displacement cut-offs for refining calculations of mean-annual energy production may inform WEC design for other sites.

Particle paths in Stokes’ edge wave

We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation which decreases with depth and distance from the shoreline. We discuss the application of this rotated coordinate frame to higher mode (Ursell) and weakly nonlinear (Whitham) edge waves, and show that the weakly nonlinear case is identical to that for two-dimensional deep-water Stokes waves.