Rodney J. Sobey

Measurements of the wind-wave energy flux in an opposing wind

A wind-wave flume which allows mechanically generated water waves to propagate in opposition to a boundary-layer air flow has been used to measure the air-flow structure in an opposing wind–wave situation. Measurements of the wave-induced pressure closely follow the predictions of potential flow theory, with the pressure in antiphase with the water surface. Hence, in contrast to the following wind situation, there is no appreciable air–water energy flux due to normal stresses. The vertical and horizontal wave-induced velocities deviate slightly in magnitude from the potential flow result while still following it qualitatively. Based on these velocity measurements it is determined that the Reynolds stress

A local Fourier approximation method for irregular wave kinematics

-\rho_{\rm a}\overline{\tilde{u}\tilde{u}}

Triple annual maximum series in wave climate analyses

is the dominant term in causing the decay of waves in opposing winds. The predicted rate of decay has a squared dependence on the wave slope and the ratio of wind speed to wave phase speed.

Wave Theory Predictions of Crest Kinematics

Abstract Significant predictive difficulties have been encountered in the estimation of crest and near-surface kinematics in irregular waves. A review of existing global approximation leads to a recognition of the central role of the free surface boundary conditions in the prediction of the near-surface kinematics. Local approximations that focus on a somewhat smaller segment of the record generally place more emphasis on the free surface boundary conditions and do not compromise local fidelity in the global interest. A local Fourier approximation method for irregular wave kinematics is introduced. The method is rational and not empirical, in that it seeks to exactly satisfy the free surface boundary conditions in a moving local window. Comparisons with predictions from steady wave theory and with laboratory measurements are excellent.

Intensity-duration-frequency summaries for wave climate

A recurring problem in wave climate analyses is the need to predict long term events from short duration records. The relative sparsity of the observational record is enhanced by judicious recognition of near-maximum events, in addition to the annual maximum events. This paper pursues the application of triple annual maximum series. Given any extreme value distribution, the theoretical distributions for the annual second largest monthly wave and the annual third largest monthly wave are established. A maximum likelihood method is proposed to fit these simultaneous distributions to the triple annual maximum series. An application of the method to the historical record at the Farallon Is. off San Francisco adopts several of the more common extreme value distributions and demonstrates the potential of triple annual maximum series in enhancing the reliability of distribution fits. Nevertheless, the common practice of extrapolating short duration records to long term events remains precarious.

Correlation between individual waves in a real sea state

In much of the practice of coastal and ocean engineering, the question of which wave theory to use has been largely of academic interest. Consideration of shallow water and/or higher order wave theories has been complicated by the relative inaccessibility of these theories. The literature is extensive and frequently confusing, which has often led to the adoption of linear wave theory, whether or not it is appropriate. In much of the practical parameter range, mathematical predictions for steady, progressive waves are available from a range of orders from Stokes, Cnoidal and Fourier theories. The differences are often considerable.

COMPLEX ENVELOPE IDENTIFICATION OF WAVE GROUPS

Abstract The relationship between sea state intensity, sea state duration and frequency is pursued in the context of wave data from five sites in US waters. A rational methodology is presented for the interpolation and extrapolation of measured trends, based on extreme value series for intensity, given duration. The inevitable short duration data base problem is addressed by routine application of the triple annual maximum methodology. A format is suggested for intensity-duration-frequency (IDF) data preparation and presentation. Examples are given for wave climate data on the Pacific, Gulf and Atlantic coasts of the United States.

Horizontal momentum jets in rotating basins

The correlation between individual waves in a real sea state has a central role in existing theories of wave grouping. The attractive Kimura (1980) theory has two critical assumptions, that the sequence of individual wave heights follows a Markov process and that the joint distribution of consecutive wave heights follows a bivariate Rayleigh form. Analysis of measured water surface records suggests that sequences of individual waves can reasonably be described as a first order mixed autoregressive, moving-average or ARMA process, though a distinction among ARMA (1,0), ARMA (0,1) and ARMA (1,1) models was beyond the resolution of the data. These include the Markov or ARMA (1,0) model. The decisive detail, the joint distribution of consecutive wave heights in the sea state, was evaluated by a simulation methodology that is consistent with the Gaussian random wave model. The estimates are dependent on spectral shape and are consistently narrower and more sharply focussed at the peak than the corresponding bivariate Rayleigh estimate. The resulting predictions of run and group length statistics differ from the Kimura theory, though not by a sufficient margin to displace the Kimura theory as a pragmatic choice for wave grouping.

ANALYTICAL SOLUTION OF NON-HOMOGENEOUS WAVE EQUATION

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.

Analytical solutions for storm tide codes

In order to prevent stagnation and improve water quality, the intakes of many water-supply reservoirs have the form of momentum jets directed approximately radially into the storage. An analysis which idealizes this flow as consisting of a turbulent jet issuing horizontally from a circular orifice into a large rotating basin of deep water shows that the jet path is a spiral whose length scale L depends upon the rate of rotation and the kinematic momentum of the jet. Good agreement is found with flow-visualization experiments when the basin depth h is ‘large’ ( h/L [gsim ] 0·21). For small depths ( h/L [lsim ] 0·024) the flow tends to be twodimensional and the jet path is found to be straight. Full-scale reservoirs are usually shallow enough that the effect of the earths rotation on the jet path is likely to be small. However these reservoirs are not inordinately shallow and tests with distorted hydraulic models are likely to show significant effects of rotation and can be misleading to the unsuspecting.