A Flexible Seafloor Carpet for High-performance Wave Energy Extraction

Similar to the mechanism by which a visco-elastic mud damps the energy of overpassing surface waves, if the near-shore seafloor is carpeted by an elastic thin material attached to generators (i.e. dampers) a high fraction of surface wave energy can be absorbed. Here we present analytical modeling of the flexible carpet wave energy converter and show that a high efficiency is achievable. Expressions for optimal damping and stiffness coefficients are derived and different modes of oscillations are discussed. The presented wave energy conversion scheme is completely under the water surface hence imposes minimal danger to boats and the sea life (i.e. no mammal entanglement). The carpet is survivable against high momentum of storm surges and in fact can perform well under very energetic (e.g. stormy) sea conditions, when most existing wave energy devices are needed to shelter themselves by going into an idle mode. I am honored to be a colleague of Prof. Ronald Yeung at the University of California, Berkeley. He is a world renowned scientist of ship hydrodynamics with several valuable and key contributions to the field. This manuscript on a new ocean wave energy extraction scheme is due to Ron’s recent interest in the field of ocean renewable energy. I am looking forward to years of working closely with him. Thank you Ron. INTRODUCTION Gade (1) reports a place in the gulf of Mexico known to locals as mud hole where due to the accretion of mud banks has turned into, for the local fishermen, a safe haven against strong waves during storms. Within the mud hole the interaction of surface waves with the mud is very strong such that waves completely damped out within a few wavelengths (2). Observations of strong wave damping due to the coupling with the bottom mud is not limited to the gulf, but almost anywhere with a muddy seafloor (e.g. 3; 4; 5). If mud can take a substantial energy out of incident surface gravity waves, an artificial carpet deployed on the seabed that responds to the action of the overpassing waves in the same way as the response of a mud-layer must be able to extract the same amount of energy. Analysis of performance of this synthetic seabed-carpet wave energy conversion technique is the subject of this article. The complicated nature of the seafloor mud and the wide range of mechanical/material properties which may be location and even time dependent, has aroused a great deal of research on this subject in the past. For understanding wave-mud interactions several models have been incorporated including, but not limited to, Newtonian (6), non-Newtonian (7; 8), viscoelastic (9; 10), porous (11), poro-elastic (12), and bottom friction (13). The correct model in general is yet a matter of dispute (14; 15), however, under the periodic forcing a viscoelastic model has been shown to be a very good approximation and is now widely used (16; 17). While the general idea presented here can incorporate any mud model, for specificity, we focus our attention on a linear viscoelastic model. In this paper we consider a seabed-carpet composed of carpet mass attached to sets of vertically acting linear springs and generators, with the generator’s action modeled to be linearly proportional to the vertical speed. We show that the coupled governing equation of waves/carpet system admits two modes 1 Copyright c © 2012 by ASME