Prediction of nearshore currents using a second-order turbulence mode

A second order turbulent closure method is implemented in the development of a two-dimensional nearshore coastal hydrodynamic model. The model predicts the mean surface elevation and the vertical profiles of the horizontal currents and turbulent stresses along a cross-shore transect of a gently sloping beach with parallel bottom contours. Known inputs to the model include wind speed and direction, air-sea temperature difference, longshore surface slope, wave field and mean water level at an initial cross-shore position, bottom roughness, and bottom topography. Since we allow vertical shearing and employ a predictive turbulence model, bottom drag and eddy viscosity coefficients, although ubiquitous in the literature, are not needed in our formulation.;Scaling arguments and commonly accepted assumptions yield a two point boundary value problem in the vertical coordinate; cross-shore variations enter parametrically through the boundary conditions and through the mean cross-shore surface slope. Standard linear wave techniques are used for simplicity in this initial effort. The response of the horizontal currents to a typical local storm condition as well as to various parameter settings is qualitatively discussed and a comparison of selected laboratory and field observations is given.;The longshore current is predicted to be substantially depth independent apart from sharp gradients near the boundaries. Under the conditions tested and observations examined, wind and longshore pressure gradients are shown to provide nonnegligible effects in forcing longshore currents. When wind forcing dominates, the longshore profiles resemble turbulent Couette flow. As wave forcing increases, they are more akin to Poiseuille flow profiles. Satisfactory agreement with observations is found.;The cross-shore current varies dramatically in the vertical, particularly in areas of substantial wave breaking. In the most seaward regions of our study, the wind can provide nonnegligible forcing in the cross-shore direction; nevertheless, this effect is smaller than in the longshore direction. The qualitative features of the vertical distribution inside and outside the surf zone are predicted; however, the numerical agreement with observations is less satisfactory than in the longshore direction. An inadequate description of the wave forcing near the surface is believed to be the cause.