David L. Kriebel

Numerical simulation of time-dependent beach and dune erosion

A computational procedure is developed for predicting the time-dependent, two-dimensional beach and dune erosion during severe storms due to elevated water levels and waves. The model employs the equation of sediment continuity and a dynamic equation governing the cross-shore sediment transport due to a disequilibrium of wave energy dissipation levels. These equations are solved numerically by an implicit, double-sweep procedure to determine the change in position of elevation contours in the profile. Given sufficient time, the profile will evolve to a form where the depth, h, in the surf zone is related to the distance seaward of the waterline by the relationship: h = Ax23, which is consistent with many natural profiles and in which A depends on sediment characteristics. The model is verified qualitatively and quantitatively through application to several idealized cases and through a preliminary simulation of erosion during Hurricane Eloise. In general, the time scales for shoreline response were found to be quite long relative to natural storm systems and erosion in the early response stages was found to be sensitive to storm surge height, but much less sensitive to wave height. The model response characteristics for simulation of erosion due to time-varying storm conditions show a lag between the maximum storm surge elevation and maximum erosion with the maximum erosion rate occurring at the time of the peak surge. For the simulated erosion due to Hurricane Eloise, reasonable agreement was found between the post-hurricane dune profiles and those calculated. However, the eroded volumes were in better agreement than the profile forms as the steepening of the natural dune profiles was not reproduced in the model.

Nonlinear wave interaction with a vertical circular cylinder. Part II: Wave run-up

Abstract Theoretical results for second-order wave run-up around a large diameter vertical circular cylinder are compared to results of 22 laboratory experiments conducted in regular nonlinear waves. In general, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around the cylinder. At the front of the cylinder, for example, measured maximum run-up exceeds linear theory by 44% on average but exceeds the nonlinear theory by only 11% on average. In some cases, both measured run-up and the second-order theory exceed the linear prediction by more than 50%. Similar results are found at the rear of the cylinder where the second-order theory predicts a large increase in wave amplitude for cases where the linear diffraction theory predicts little or no increase. Overall, the nonlinear diffraction theory is found to be valid for the same relative depth and wave steepness conditions applicable to Stokes second-order plane-wave theory. In the last section of the paper, design curves are presented for estimating the maximum second-order wave run-up for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness.

Nonlinear wave interaction with a vertical circular cylinder. Part I: Diffraction theory

Abstract A closed-form solution is developed for the velocity potential resulting from the interaction of second-order Stokes waves with a large vertical circular cylinder. At first-order, the solution is the usual linear diffraction theory. At second-order, the solution consists of forced wave motions, due to nonlinear wave-wave interactions in the free surface boundary condition, plus scattered free wave motions, due to the interaction of the forced waves with the fixed cylinder. The velocity potentials are then used to determine the theoretical free surface elevations around the cylinder consistent to second-order. Second-order terms are found to significantly alter wave envelopes around the cylinder as a result of nonlinear diffraction. For example, the maximum wave crest run-up on the cylinder from the nonlinear theory is found to exceed that predicted by the linear diffraction theory by up to 50%. A brief comparison of the nonlinear theory with the measured run-up data is found to largely confirm the theoretical solution.

Nonlinear Effects on Wave Groups in Random Seas

Laboratory simulations of extreme random seas reveal that high wave crests occur more frequently than predicted by the Rayleigh distribution. In this paper, a theory is presented to account for nonlinearities in the sea state to second-order resulting in a non-Rayleigh distribution of wave crest and trough amplitudes based on the narrow-band assumption. The resulting probability density function are then used to predict average wave group characteristics through a modification of linear wave envelope theory which accounts, for example, for a significant decrease in the time intervals between successive runs of high crests compared to linear theory. The nonlinear theory is then verified based on a laboratory data set on deep water wave group statistics for severe seas described by Bretschneider and JONSWAP spectra.

UNDISTORTED FROUDE MODEL FOR SURF ZONE SEDIMENT TRANSPORT

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.

BEACH AND DUNE RESPONSE TO SEVERE STORMS

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 TRANSMISSION PAST VERTICAL WAVE BARRIERS

A study of alternatives including a shoreline evolution numerical modelization has been carried out in order to both diagnose the erosion problem at the beaches located between Cambrils Harbour and Pixerota delta (Tarragona, Spain) and select nourishment alternatives.

WAVE RUNUP ON COMPOSITE-SLOPE AND CONCAVE BEACHES

A special reflecting wall 12 m long and 2.1 m high was built off the beach at Reggio Calabria, and 30 wave gauges were assembled before the wall and were connected to an electronic station on land. It was possible to observe the reflection of wind waves generated by a very stable wind over a fetch of 10 Km. The experiment aimed to verify the general closed solution for the wave group mechanics (Boccotti, 1988, 1989), for the special case of the wave reflection.Significant features on Wadden Sea wave climate are evaluated in respect of the state of the art. Main emphasis was laid on an analysis of the governing boundary conditions of local wave climate in island sheltered Wadden Sea areas with extensions being sufficient for local wind wave growth. Explanatory for significant wave heights a reliable parametrization of local wave climate has been evaluated by using generally available data of water level and wind measurements.

Mooring Loads Due to Parallel Passing Ships

Laboratory tests were conducted to measure the loads on a moored ship resulting from a passing ship moving parallel to the moored vessel. The tests included changes in the passing vessel speed, vessel displacement, water depth, and separation distance between the two ships. Measurements were made of the surge forces, sway forces, and yaw moments. Two existing predictive models were evaluated in “blind” tests to determine their ability to predict the measured mooring loads. A new set of empirical equations are then proposed that provide improved descriptions of the measured peak mooring loads.

BREAKING WAVES IN LABORATORY-GENERATED JONSWAP SEAS

Abstract Results from a laboratory study of wave breaking in deep-water random seas are presented for approximate JONSWAP sea states. Waves generated at one end of a 116-meter wave tank are observed for breaking at a section of the tank approximately 30 meters from the wavemaker and in regions spanning three and six meters about the section. Emphasis is on the relative number of breaking waves observed at the section and in the regions about it, and on the relative number of crest amplitudes exceeding specified levels at the section. Measurements at the section are shown to be in good agreement with predictions formed using idealized assumptions about the breaking waves and a modified Rayleigh distribution of crest amplitudes that accounts approximately for nonlinear effects in seas with narrow-banded wave frequencies. Results indicate that the average downward crest acceleration of breaking waves in these sea states is equal approximately to one-third the acceleration of gravity. Experimental measurements of breaking in regions about the section are shown to be in good agreement with theoretical predictions relating breaking events over a region to those at a fixed location.