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Regular version of the site

Article

On the use of linear theory for measuring surface waves using bottom pressure distribution

European Journal of Mechanics - B/Fluids. 2018. Vol. 67. No. 1. P. 97-103.
Pelinovsky E., Touboul J.

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.