Wave transformation by a dredge excavation pit for waves from shallow water to deep water

• Analytic solution to EMMSE is given for wave transformation over a dredge excavation pit.
• With the validity in the whole wave range, the solution is better to long wave solution.
• Without approximation to the pit sidewall, the present solution is exact about topography.
• Influences of pit dimension and wave period on relative amplitude are intensively studied.

In this paper, an analytic study on wave scattering by a dredge excavation pit is conducted, where the pit is assumed to be axi-symmetric and idealized with its depth profile in radial distance being a simple power function. By using techniques of variable separation and series expansion, a series solution to the explicit modified mild-slope equation (EMMSE) is constructed and the convergence condition is clarified. It is clear that this analytic solution is valid in the whole wave spectrum from shallow-water waves to deep-water waves due to the use of the EMMSE, which is superior to previous long-wave analytic solutions. Based on this analytic solution, influences of the pit dimension including its depth, bottom radius and opening radius on relative wave amplitude (i.e., the wave amplitude relative to the incident amplitude) are investigated. It is shown that the pit size plays a more important role than the sidewall steepness does in affecting the wave pattern. With the broader validity than that of the long-wave model, it is found that the wave attenuation within and in the lee side of the pit intensifies first and then decreases as the incident waves becomes short.