Journal of Waterway, Port, Coastal, and Ocean Engineering

This paper and its companion paper describe the development of a finite-element model based on modified Boussinesq equations and the applications of the model to harbor resonance problems. This first of the two papers reports the model development and validations. A Galerkin finite-element method with linear elements is employed in the model. Auxiliary variables are introduced to remove the spatial third derivative terms in the governing equations, and an implicit predictor-corrector iterative scheme is used in the time integration. The treatments of various boundary conditions, including the perfect reflecting boundary with an irregular geometry, the absorbing (sponge layer) boundary, and the incident wave boundary, are described. Numerical results are obtained for several examples, and their accuracy is checked by comparing numerical results with either experimental data or analytical solutions.

The finite-element model for modified Boussinesq equations developed in Part I of this paper is used to study harbor resonance problems. The internal wavemaker technique is implemented on an unstructured finite-element mesh, and a sponge layer is used as an open boundary condition. Both linear and nonlinear harbor oscillations in rectangular and circular basins are examined, and experimental measurements and analytical solutions are used to validate the model. Finally, the wavelet transform is employed to analyze transient features of the nonlinear resonance problem.

A new parameter is proposed to characterize the tail spreading performance of extremal distribution functions as defined by the ratio of the 50-year return wave height to the 10-year height, and it is called the spread parameter. Extreme data sets of annual maximum wind speed and peaks-over-threshold significant wave heights have been analyzed for best-fitting distribution functions, for which the spread parameter is evaluated. The observed values of the spread parameter are in good agreement with the predicted values based on the coefficient of variation of an extreme data sample. Formulas are given to derive the scale and location parameters from a given value of the spread parameter. Some typical values of the spread parameter are presented for promotion of performance-based design of maritime structures in the world.

The application of Stokes fifth-order wave theory to random deep-water waves is considered in connection with nonlinearity in crest amplitudes. The theory is shown to apply, on average, to crest amplitudes and wave heights, although differences exist for individual waves as a result of variation in wave frequency. Corrections to the Rayleigh law and associated predictions of fractions of waves exceeding crest threshold levels are shown to be in close agreement with measurements for heavy seas when the significant wave height and average wave period are specified accurately.

During certain meteorological events, water level oscillations up to 1.5 m with periods of less than 2 h have been observed in the Great Lakes. The squall line events of 7–11 March 1998, 29 May–2 June 1998, and 8–12 November 1998 in Lake Michigan, are analyzed by spectral and analytical methods. Dominant periods of less than 2 h are identified in the spectra of water level fluctuations and coherencies among the spectral peaks of water levels of different station pairs are calculated to determine whether the oscillations are localized or basin wide. Explicit numerical calculations of normal mode periods and structures using a Lanczos procedure show that the dominant periods in the observed data are consistent with the structures and periods of some of the calculated modes. The March 1998 and the November 1998 episodes show higher surges with a gradual rise of water level, while the episode of May 1998 shows an abrupt rise in the water level at Calumet Harbor and about ten times higher spectral signature than the former two. Many of the high-frequency modes have large amplitude at or near Calumet Harbor and the periods are close to the periods of edge waves that would be generated by a squall line similar to the May 1998 squall line. The trapping of energy and localized higher modes in a water body can work together to excite edge waves and localized seiches causing abrupt water level fluctuations.

Three forms of the hydraulic Escoffier curve relating the cross-sectional area of a tidal inlet to it’s connecting channel velocity are discussed along with assumptions and simplifications. Examples are provided of the methods for the same inlet parameters. These examples show large variability in the inlet stability depending on the method chosen. A recommendation is provided for the optimal methodology along with rationale for the choice.

A hydrodynamic analysis has been conducted to assess the potential impact of the sea state on cargo transfer operations in simultaneous sea and swell waves incident from distinct directions. An interactive tool has been developed that allows parameter variation and provides an immediate graphical presentation of the data. This note presents some typical results for relative vertical velocity between two of the vessels in the form of surface and polar plots. These graphical representations clearly display the effects of shielding and other complex hydrodynamic interactions among the vessels in a seaway.