Development of two-dimensional models to estimate nearshore bathymetry and sediment transport.

摘要

We examine the interactions and feedbacks between bathymetry, waves, currents, and sediment transport. Utilizing remotely-sensed wave refraction patterns of nearshore waves, we estimate bathymetry gradients in the nearshore through the 2D irrotationality of the wave number equation. The model, discussed in Chapter 2, uses an augmented form of the refraction equation that relates gradients in bathymetry to gradients in wavenumber and wave angle through the chain rule. The equations are cast in a form that is independent of wave period, so can be solved using wavenumber and direction data from a single snapshot rather than the normally-required time series of images.;Secondly, remotely sensed images of wave breaking over complex bathymetry are used to study the nonlinear feedbacks between two-dimensional (horizontal), 2DH, morphology and cross-shore migration rates of the alongshore averaged bar. We first test a linear model on a subset of 4 years of data at Palm Beach, Australia. The results are discussed in Chapter 3. The model requires eight free parameters, solved for using linear regression of the data to model the relationship between alongshore averaged bar position, x, alongshore sinuosity of the bar, a, and wave forcing, F = H2o. The linear model suggests that 2DH bathymetry is linked to cross-shore bar migration rates. Nevertheless, the primary limitation is that variations in bar position and variability are required to be temporally uncorrelated with forcing in order to achieve meaningful results.;In Chapter 4 a nonlinear model is subsequently developed and tested on the same data set. Initial equations for cross-shore sediment transport are formulated from commonly accepted theory using energetics-type equations. Cross-shore transport is based on the deviations around an equilibrium amount of roller contribution with the nonlinearity of the model forcing sediment transport to zero in the absence of wave breaking. The extension to 2DH is based on parameterizations of bar variability and the associated 2DH circulation. The model has five free parameters used to describe the relation between alongshore averaged bar position, x, 2DH bar variability, a, and wave characteristics (wave height, H, wave period, T, and wave angle, theta. The model is able to span multiple storms, accurately predicting bar migration for both onshore and offshore events. The longest individual data set tested is approximately 6 months. Using manually determined values for the coefficients, bar position is predicted with an R2 value of 0.42 over this time period. The effect of including a 2D dependency both increased rates of onshore migration and prevented highly 2D systems from migrating offshore under moderate wave heights. The model is also compared against a 1DH version by setting the 2D dependency term to unity and using the same values for the five free parameters.;The last project (Chapter 5) explored the utilization of changes in bathymetry, Delta h/Deltat, to gain further understanding of the feedbacks between 2D sediment transport patterns, Qx and Qy, with respect to existing bathymetry in the nearshore. The model is based on the 2D continuity equation that relates changes in bathymetry to gradients in the cross-shore, ∂Q x/∂x, and the alongshore, ∂Qy/∂y, directions. The problem is under-determined, having two unknowns (Qy and Qx) and only one known (Deltah/Deltat) such that a series of constraints must be applied in order to solve for transport. We assume that that the cross-shore integral of Qx is closed, such that no sand enters or exits the system in this direction. By conservation of mass, this requires changes in volume of the cross-shore transect to be due to longshore gradients in Qy. We test six rules for distributing Qy: three rules describing the initial longshore transport ( Qry ) and three describing the cross-shore distribution of the excess volume component ( Qey ). Initial results suggest that requiring sediment to travel down slope ( Qrh=fBy ) is an intuitive choice for describing transport of distinct perturbations. (Abstract shortened by UMI.)