Direct numerical calculation of wave properties

Chappelear, J. E.

doi:10.1029/jz066i002p00501

Cited by 71 publications

(31 citation statements)

References 2 publications

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“…The numerical method depends for its accuracy on the ability of a Fourier series to describe the wave train. This approach was originated by Chappelear (1961) and Dean (1965), but the method Annu. Rev.…”

Section: Physical Plane Methodsmentioning

confidence: 99%

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Strongly Nonlinear Waves

Schwartz¹,

Fenton²

1982

Annu. Rev. Fluid Mech.

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Section: Physical Plane Methodsmentioning

confidence: 99%

“…The complexity of the manipulations makes a manual high order calculation impractical. Fifth-order solutions have been obtained by De (1955), Chappelear (1961), who claimed mistakes in De's solution, and by Skjelbreia & Hendrickson (1961).…”

Section: The Canonical Problem: Steady Wavesmentioning

confidence: 96%

Strongly Nonlinear Waves

Schwartz¹,

Fenton²

1982

Annu. Rev. Fluid Mech.

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“…The simplest form is the depthwise constant current under sinusoidal wave [8,9], which is extended for nonlinear waves in [10] by using velocity potential and in [11] by using stream function. Wave diffraction over a shoal-and wave-constant current interaction was studied in [12].…”

Section: Literature Reviewmentioning

confidence: 99%

Effect of vertically logarithmic steady currents on shallow surface waves

Patil

Singh

2008

Phys Oceanogr

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The combined wave-current flow has been solved by researchers by assuming wave over either depthwise constant or linear current profile. Some complicated nonlinear current profiles have also been considered to simulate various shear currents. We consider a nonlinear current vertically logarithmic in nature and examine its interaction with a periodic surface wave. The Navier-Stokes equations for incompressible flow are solved for the current part and by using periodic boundary conditions. The effect of logarithmic current on wave components is assessed. The corresponding celerity and dispersion equation yields a close-form solution for the shallowwave approximation. Several comparative trends between wave-only, wave with log current, and wave with constant current for the wave following/opposing these currents have been discussed. The flow properties of the first order are presented which can be applicable to the real inland and coastal flows, where progressive waves are ubiquitous over a depthwise logarithmic current. The work is further extended to the second-order semiempirical wave component by using past experimental data on the wave spectrum of combined flow.

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“…These theories are based on methods for approximating the nonlinear free surface boundary conditions. Examples of such theories include the Stokes fifth-order and Chappelear (1961) theories, the regular stream function theory (Dean, 1965), and the diagonal matrix version of the extended velocity potential or EXVP-D theory (Lambrakos and Brannon, 1974).…”

Section: Undlrectional Wave Analysismentioning

confidence: 99%

Storm Wave Kinematics

Forristall¹,

Ward²,

Borgman³

et al. 1978

Offshore Technology Conference

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The usual method of calculating design hydrodynamic forces on a template-type structure involves the prediction of water particle velocities and accelerations from a design wave height and period. The forces on elements are then calculated from that description of the wave kinematics. Much theoretical effort has been devoted to the vital step of developing wave theories with which to predict the kinematics from the surface description of the waves. However, until recently, instrumentation permitting verification of the theories under realistic conditions has not existed. Measurements made with a wave staff and electromagnetic current meters in tropical storm Delia in the Gulf of Mexico in 1973 were apparently the first measurements of wave kinematics under storm conditions. Comparisons of these measured velocities with those predicted by unidirectional theories commonly used in design practice showed considerable scatter and a bias toward overprediction. However, velocity statistics and spectra predicted using directional spectral concepts and linear theory compared satisfactorily with the data. The comparisons support the conclusion that it is more important for a wave theory to include directional spreading effects than to account properly for the nonlinear free surface boundary conditions.

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Direct numerical calculation of wave properties

Cited by 71 publications

References 2 publications

Strongly Nonlinear Waves

Strongly Nonlinear Waves

Effect of vertically logarithmic steady currents on shallow surface waves

Storm Wave Kinematics

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