Sung B. Yoon

Nonlinear refraction–diffraction of waves in shallow water

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K–P equation (Kadomtsev & Petviashvili 1970) to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data (Whalin 1971) and previous numerical calculations (Madsen & Warren 1984).

INTERACTIONS OF CURRENTS AND WEAKLY NONLINEAR WATER WAVES IN SHALLOW WATER

Two-dimensional Boussinesq-type depth-averaged equations are derived for describing the interactions of weakly nonlinear shallow-water waves with slowly varying topography and currents. The current velocity varies appreciably within a characteristic wavelength. The effects of vorticity in the current field are considered. The wave field is decomposed into Fourier time harmonics. A set of evolution equations for the wave amplitude functions of different harmonics is derived by adopting the parabolic approximation. Numerical solutions are obtained for shallow-water waves propagating over rip currents on a plane beach and an isolated vortex ring. Numerical results show that the wave diffraction and nonlinearity are important in the examples considered.

Resonant reflection of shallow-water waves due to corrugated boundaries

One-dimensional, nonlinear, shallow-water wave equations are derived from two-dimensional Boussinesq equations to investigate resonant reflections due to corrugated boundaries. Small, but short-wave undulations are introduced through water depth and channel width. Coupled nonlinear equations for the transmitted and reflected wave fields are derived and solved numerically. In the simple case where undulations are zero (the reflection is also zero), the governing equations are used to study the propagation of permanent shallow-water waves (cnoidal waves) and to examine the generation of higher harmonics in shallow-water waves. The present numerical results show that the nonlinear effects are very important in considering the resonant reflection of cnoidal waves from a rippled bed.

A note on Hamiltonian for long water waves in varying depth

Abstract The Hamiltonian for two-dimensional long waves over a slowly varying depth is derived. The vertical variation of the velocity field is obtained by using a perturbation method in terms of velocity potential. Employing the canonical theorem, the conventional Boussinesq equations are recovered. The Hamiltonian becomes negative when the wavelength becomes short. A modified Hamiltonian is constructed so that it remains positive and finite for short waves. The corresponding Boussinesq-type equations are then given.

COMBINED REFRACTION-DIFFRACTION OF NONLINEAR WAVES IN SHALLOW WATER

This report will update the coastal zone practitioner on the National Flood Insurance Program (NFIP) as it affects the implementation of manmade changes along the coastline. It is our intent to place in proper perspective this fast-changing and often difficult to interpret national program. Readers will achieve an overall understanding of the NFIP on the coast, and will be in a position to apply the programs requirements in their efforts. We will begin with a history of the application of the NFIP to the coastal zone. The history of the problems encountered will lead into current regulations, methodologies, and the changes the Federal Emergency Management Agency plans for the future.The spatial variability of the nearshore wave field is examined in terms of the coherence functions found between five closely spaced wave gages moored off the North Carolina coast in 17 meters depth. Coherence was found to rapidly decrease as the separation distance increased, particularly in the along-crest direction. This effect is expressed as nondimensional coherence contours which can be used to provide an estimate of the wave coherence expected between two spatial positions.Prediction of depositional patterns in estuaries is one of the primary concerns to coastal engineers planning major hydraulic works. For a well-mixed estuary where suspended load is the dominant transport mode, we propose to use the divergence of the distribution of the net suspended load to predict the depositional patterns. The method is applied to Hangzhou Bay, and the results agree well qualitatively with measured results while quantitatively they are also of the right order of magnitude.

WAVE AND CURRENT INTERACTIONS IN SHALLOW WATER

More than 150 tests have been analyzed in order to describe the dynamically stable profiles of rock slopes and gravel beaches under wave attack. Relationships between profile parameters and boundary conditions have been established. These relationships have been used to develop a computer program. This program is able to predict the profiles of slopes with an arbitrary shape under varying wave conditions, such as those found in storm surges and during the tidal period.This paper investigates the utility of winds obtainable from a numerical weather prediction model for driving a spectral ocean-wave model in an operational mode. Wind inputs for two operational spectral wave models were analyzed with respect to observed winds at three locations in the Canadian east coast offshore. Also, significant wave heights obtainable from the two spectral models were evaluated against measured wave data at these locations. Based on this analysis, the importance of appropriate wind specification for operational wave analysis and forecasting is demonstrated.