In a time of climate emergency due to global warming, nature-based coastal defence systems are attractive solutions for flood mitigation and adaptation. Coastal forests such as mangroves have received a growing interest for their disaster mitigation effectiveness such as water flow energy dissipation, hence helping communities to become more resilient (Iimura & Tanaka, 2012). The role of coastal forests as a defence measure was highlighted in the aftermath of the 2004 Indian Ocean Tsunami, which claimed the lives of more than 200,000 people and displaced millions more across fourteen countries. Post-disaster damage observations indicated that forests, particularly mangroves, reduced the impact of the tsunami wave in some locations. As a result, significant international relief and reconstruction efforts focused on extensive forest replantation of coastlines (Satake, 2014).

The role of coastal vegetation in reducing the severity of tsunami waves has been studied since. Several studies using physical modelling and computational approaches have provided insights into the wave attenuation provided by coastal vegetation, in terms of relationships between incident hydrodynamic conditions, forest configurations and wave height decay. However, there are still many gaps in knowledge, particularly in quantifying the efficacy of coastal forests in reducing inland hydrodynamic conditions (Tomiczek et al., 2020). It is therefore essential to improve the understanding on how wave heights, velocities and runup are influenced by the characteristics of the “obstacles”, e.g. the forest density, as well as the incident hydrodynamic conditions, e.g. the wave period. This study aims to address these questions conducting physical experiments using the novel pneumatic Tsunami Simulator (TS) developed by HR Wallingford together with UCL (Rossetto et al., 2011).

This paper examines 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.