The Influence of Free Long Wave Generation on the Shoaling of Forced Infragravity Waves

Theo Moura,Tom E Baldock

doi:10.3390/jmse7090305

Abstract

Different conceptual models for forced infragravity (long) waves exist in the literature, which suggest different models for the behavior of shoaling forced waves and the possible radiation of free long waves in that process. These are discussed in terms of existing literature. A simple numerical model is built to evaluate the wave shape in space and time during shoaling of forced waves with concurrent radiation of free long waves to ensure mass continuity. The same qualitative results were found when performing simulations with the COULWAVE model using the radiation stress term in the momentum equation to force the generation and propagation of bound waves. Both model results indicate a strong frequency dependence in the shoaling rate and on the lag of the total long wave with respect to the forcing, consistent with observations in the literature and more complex evolution models. In this approach, a lag of the long wave is only observed in the time domain, not in the space domain. In addition the COULWAVE is used to investigate dissipation rates of incident free and forced long waves inside the surf zone. The results also show a strong frequency dependence, as previously suggested in the literature, which can contribute to the total rate of decay of the incident forced wave after short wave breaking.

Highlights

The importance of forced long waves, or bound waves, to the oceans dynamics is well established in the literature, especially in shallow waters
The results presented for this conceptual model are quite simple, but they indicate that adding waves into the bound wave shoaling process may change the results and the interpretation of free waves into and the phase boundlags wave shoaling process may change the results and the energy transfers, of the forced wave
Dissipation of free long waves by eddy turbulence inside a surf zone is certainly frequency dependent based on the COULWAVE model, and it is likely this explains the decay of the incident forced wave as proposed by Battjes et al [13], with some additional reduction in amplitude since the forcing is being reduced by short wave breaking

Summary

Introduction

The importance of forced long waves, or bound waves, to the oceans dynamics is well established in the literature, especially in shallow waters. Nielsen and Baldock [8]With presented simple to the response ofthen the shoaling (an increase in amplitude in shallower water) does not necessarily require radiation free surface elevation to both non-resonant (finite water depth conditions) and resonant (shallow of water waves to ensure continuity volume, but with a has bound pureconditions depression, increase conditions) radiation stress of forcing. This solution thewave same of initial asthen thoseanproposed in amplitude of that depression requires radiation of free waves to ensure continuity.

Bound Wave Shoaling

Bound Wave Dissipation after Short Wave Breaking

Incident

Discussion