Gravity waves over porous bottoms

Abstract

Water wave interactions with porous seabeds of granular material were investigated theoretically and experimentally. An assessment on the nature of the resistances in a general, unsteady, porous flow model showed that Darcy's law (linear resistance only) has a very limited application under a natural wave environment; in most cases, inertial and nonlinear resistances should be considered. The case of a linear wave system over a rigid porous bed of finite depth was solved to facilitate comparisons with the experiment. The solutions on wave damping and on wave kinematics (change of wave period or wave length) are quite different from those of available solutions. The maximum wave damping was found to occur when the dissipative resistance (velocity related) is equal to the nondissipative resistance (acceleration related). In the experiment, twelve different porous gravel beds with three water depths (a total of 36 cases) were tested under a standing wave system. The virtual mass coefficient, C a, determined from the experiment data was 0.46 rather than zero as assumed in some publications. The predicted values of this study agree much better with the experiment data than those of the available solutions. The tests were also extended to two extreme cases: beds with thickness of a single grain size and a bed of fine sand. In both cases, the wave kinematics are only slightly affected. However, the damping characteristics are significantly altered. In the former case, the boundary layer effect apparently could no longer be ignored, whereas in the latter case the movement of sand particles caused the rate of damping to increase by several orders of magnitude.