The Submarine Equilibrium Profile: A Physical Model

Abstract

The Submarine Profile (SP) is the sea floor profile normal to the coast line, located between the surf zone and wave base and formed by wave action on the clastic sediment. The Submarine Equilibrium Profile (SEP) is a SP where geometry and sediment movement are in a quasi equilibrium status with offshore nominal waves (the large swell dominating this area). The geometry of the SEP has been identified qualitatively and conceptually as a concave upward smooth curve. The slope of SEP becomes gentler and gentler offshore until it is almost horizontal at the so-called wave base. Some empirical equations have been proposed and are used widely in engineering. This report summarizes previous field observations, lab experiments and theories concerning mechanisms involved in the formation of this geometry. A series of physical equilibrium conditions, including the major mechanical forces involved in particle movement, are used to derive an analytical model. This model expresses the geometry of the SEP in an explicit form where x is a function of y, in relation with the offshore wave period (or wave length). The basic idea has been qualitatively tested in a wave tank experiment. The final equation was then tested and calibrated on a number of submarine profiles plotted from three marine basins around the U.S. using a non-linear regression algorithm. The profiles located on the U.S. coasts along the Gulf of Mexico and on southeast U.S. Atlantic coasts were selected following geological and visual criteria which previous researches used to characterize the SEP concept. The comparison between the theoretical equation and the selected Gulf of Mexico and Atlantic profiles by a non-linear computer regression process showed a satisfactory match with high correlation coefficients. The Pacific profiles, located in an area with ongoing active tectonic movement are generally not in SEP status and have more features deviating from the conceptual and SEP physical models. The wave periods obtained from the nonlinear regression process for some SEP's on the Gulf of Mexico coast are further compared with the available hindcast offshore wave data published in 1989. The results of these comparisons are generally encouraging, except those comparisons involving SP's on the U.S. Pacific coast.