Long waves propagating over a circular bowl pit

Abstract

An analytic solution to the mild slope wave equation is derived for long waves propagating over a circular, bowl-shaped pit located in an otherwise constant depth region. The analytic solution is shown to reduce to a previously derived analytic solution for the case of a bowl-shaped enclosed basin and to agree well with a numerical solution of the hyperbolic mild-slope equations. The effects of the pit dimensions on wave scattering are discussed based on the analytic solution. This analytic solution can also be applied to pits of different general shapes. Finally, wave attenuation in the region over the pit is discussed.

An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit

“…Later, Suh et al [13] found that the MSE solution does not agree with the exact FEM solution even for slopes less than 1:3. They found that this disagreement is primarily due to the slope discontinuity at both ends of the slope that can be represented by the bottom curvature term of the EMSE.…”

“…On the other hand, Suh et al [13] presented the analytic solution for long waves propagating over a parabolic pit, in which the water depth varies in proportion to the second power of the radial distance from the pit center. The present study is to extend the Suh et al's solution by easing the restriction on bathymetry.…”

An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit

“…On the other hand, in the case of a parabolic pit ( 2 = α ), Suh et al (2005) showed that wave attenuation occurred in such a way that the wave amplitude became smaller than the incident amplitude in the region over the pit. Fig.…”

“…On the other hand, Suh et al (2005) presented an analytic solution for long waves propagating over an axi-symmetric pit where the water depth decreases from the center to the edge in proportion to the second power of the radial distance from the pit center. In the present study, first, the restriction on topography in Suh et al's solution is eased by making the water depth inside the pit vary in proportion to any integer power of the radial distance; the first power corresponds to a conical pit and the pit approaches to a cylindrical pit as the power increases.…”

A long waves propagation in two-layer fluid over a circular bowl pit

“…Then, as a verification processes, the new analytic solution in a special case of the two-layer fluid model, i.e 1= 0 with the solution in single-layer fluid model obtained by Suh et. al [11]are compared. Using the new solution, the effects of the pit dimensions on the wave refraction are discussed.…”