On the use of linear theory to estimate bottom pressure distribution under nonlinear surface waves

- Travelling solitonic waves, and transient wave packets are propagated numerically using two distinct approaches.
- The first one is based on fully nonlinear potential equations, while the second one is based on the Green-Naghdi system of equations.
- Bottom pressure distributions are compared to both space and time linear theory.
- Qualitative and quantitative behaviour are compared. The role of dispersion in the physical process is emphasized.

The bottom pressure distribution beneath large amplitude waves is studied within linear theory in time and space domain, weakly dispersive Serre-Green-Naghdi system and fully nonlinear potential equations. These approaches are used to compare pressure fields induced by solitary waves, but also by transient wave groups. It is shown that linear analysis in time domain is in good agreement with Serre-Green-Naghdi predictions for solitary waves with highest amplitude A=0.7h, h being water depth. In the meantime, when comparing results to fully nonlinear potential equations, neither linear theory in time domain, nor in space domain, provide a good description of the pressure peak. The linear theory in time domain underestimates the peak by an amount similar to the overestimation by linear theory in space domain. For transient wave groups (up to A=0.52h), linear analysis in time domain provides results very similar to those based on the Serre-Green-Naghdi system. In the meantime, linear theory in space domain provides a surprisingly good comparison with prediction of fully nonlinear theory. In all cases, it has to be emphasized that a discrepancy between linear theory in space domain and in time domain was always found, and presented an averaged value of 20%. Since linear theory is often used by coastal engineers to reconstruct water elevation from bottom mounted sensors, the so-called inverse problem, an important result of this work is that special caution should be given when doing so. The method might surprisingly work with strongly nonlinear waves, but is highly sensitive to the imbalance between nonlinearity and dispersion. In most cases, linear theory, in both time and space domain, will lead to important errors when solving this inverse problem.