Dimitris Stagonas

We examine experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional  1D+1 constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from 0 to -0,87 s-1 For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the 95% confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between 0 and -0.48 s-1. Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE.

The role of recurves on top of seawalls in reducing overtopping has been previously shown but their influence in the distribution and magnitude of wave-induced pressures and forces on the seawall remains largely unexplored. This paper deals with the effects of different recurve geometries on the loads acting on the vertical wall. Three geometries with different arc lengths, or extremity angles (α_e), were investigated in large-scale physical model tests with regular waves, resulting in a range of pulsating (non-breaking waves) to impulsive (breaking waves) conditions at the structure. As the waves hit the seawall, the up-rushing flow is deflected seawards by the recurve and eventually, re-enters the underlying water column and interacts with the next incoming wave. The re-entering water mass is, intuitively, expected to alter the incident waves but it was found that the recurve shape does not affect wave heights significantly. For purely pulsating conditions, the influence of α_e on peak pressures and forces was also negligible. In marked contrast, the mean of the maximum impulsive pressure and force peaks increased, even by a factor of more than two, with the extremity angle. While there is no clear relation between the shape of the recurve and the mean peak pressures and forces, interestingly the mean of the 10% highest forces increases gradually with α_e and this effect becomes more pronounced with increasing impact intensity.