A Parametric Wind Wave Model for Arbitrary Water Depths

Graber, Hans C.; Madsen, Ole Secher

doi:10.1007/978-94-015-7717-5_25

Cited by 3 publications

(2 citation statements)

References 78 publications

(108 reference statements)

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“…In finite water depth, Graber [] following Kitaigordskii et al [] derived a finite‐depth JONSWAP spectrum, which can be expressed as

S_{η η} = ϕ (ω) S_{J}

where

ϕ (ω) = χ^{- 2} {true[1 + ω^{2} \frac{h}{g} (χ^{2} - 1) true]}^{- 1}

in which h is water depth and χ is obtained from

χ \tanh (\frac{h ω^{2}}{g} χ) = 1

…”

Section: Experimental Conditionsmentioning

confidence: 99%

Turbulent boundary layers under irregular waves and currents: Experiments and the equivalent‐wave concept

Yuan

2016

JGR Oceans

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A full-scale experimental study of turbulent boundary layer flows under irregular waves and currents is conducted with the primary objective to investigate the equivalent-wave concept by Madsen (1994). Irregular oscillatory flows following the bottom-velocity spectrum under realistic surface irregular waves are produced over two fixed rough bottoms in an oscillatory water tunnel, and flow velocities are measured using a Particle Image Velocimetry. The root-mean-square (RMS) value and representative phase lead of wave velocities have vertical variations very similar to those of the first-harmonic velocity of periodic wave boundary layers, e.g., the RMS wave velocity follows a logarithmic distribution controlled by the physical bottom roughness in the very near-bottom region. The RMS wave bottom shear stress and the associated representative phase lead can be accurately predicted using the equivalent-wave approach. The spectra of wave bottom shear stress and boundary layer velocity are found to be proportional to the spectrum of free-stream velocity. Currents in the presence of irregular waves exhibit the classic two-log-profile structure with the lower log-profile controlled by the physical bottom roughness and the upper log-profile controlled by a much larger apparent roughness. Replacing the irregular waves by their equivalent sinusoidal waves virtually makes no difference for the coexisting currents. These observations, together with the excellent agreement between measurements and model predictions, suggest that the equivalent-wave representation adequately characterizes the basic wave-current interaction under irregular waves.

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“…In finite water depth, Graber [] following Kitaigordskii et al [] derived a finite‐depth JONSWAP spectrum, which can be expressed as

S_{η η} = ϕ (ω) S_{J}

where

ϕ (ω) = χ^{- 2} {true[1 + ω^{2} \frac{h}{g} (χ^{2} - 1) true]}^{- 1}

in which h is water depth and χ is obtained from

χ \tanh (\frac{h ω^{2}}{g} χ) = 1

…”

Section: Experimental Conditionsmentioning

confidence: 99%

Turbulent boundary layers under irregular waves and currents: Experiments and the equivalent‐wave concept

Yuan

2016

JGR Oceans

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“…The finite-depth Joint North Sea Wave Project (JON-SWAP) spectrum proposed by Graber (1984) and Bouws et al (1985), also known as the TMA spectrum, is adopted here to construct unimodal and bimodal wave spectra whose bottom velocity spectra take the form of…”

Section: Comparisons Of Spectral and Equivalent Wave Models A Bottom ...mentioning

confidence: 99%

A Simple Model for Random Wave Bottom Friction and Dissipation

Zou¹

2004

J. Phys. Oceanogr.

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Based on the spectral eddy viscosity model of bottom boundary layers, the spectral representation of bottom friction and dissipation for irregular waves is reduced to an equivalent monochromatic wave representation. The representative wave amplitude and frequency are chosen so that the bottom velocity and bottom shear stress variances of the equivalent wave model are identical to those of the spectral model. Moreover, these variances have to satisfy the same relationship as those of a monochromatic wave with the same frequency. According to the wave bottom boundary layer theory, the ratio between bottom stress spectrum and bottom velocity spectrum has a frequency dependence of q , where the exponent q is a positive constant. The representative wave frequency and direction are obtained based on this power law, whereas in previous studies they were derived using a Taylor expansion of the ratio about a particular frequency or were proposed heuristically. Previous equivalent wave theories are therefore valid only for narrowbanded wave spectra. The present theory, however, is applicable to a wide variety of wave spectra including broadbanded and multimodal spectra.

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Waves and currents over a fixed rippled bed: 3. Bottom and apparent roughness for spectral waves and currents

Mathisen¹,

Madsen²

1999

J. Geophys. Res.

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Abstract. This paper is the third in a series of three that presents the results of experiments designed to verify the use of a single bottom roughness length scale for waves and currents over a rough bed. While the first two papers concentrated on the bottom roughnesses experienced by monochromatic wave and current boundary layer flows, this paper presents the results of additional experiments that investigate the use of an equivalent wave representation to extend these results to spectral wave and current boundary layer flows. Spectral waves, simulated by five components, and currents were generated in a 20-m-long wave flume with a fixed rippled bottom. Attenuation due to bottom friction is determined from total attenuation measurements for individual wave components by removing the effects of sidewall dissipation and wave-wave interactions. These attenuation estimates are used to establish representative friction factors, which are used in conjunction with an existing eddy viscosity model to determine bottom roughnesses. The bottom roughnesses experienced by spectral waves (in the presence and absence of a current) match the bottom roughnesses for monochromatic waves. When these experimentally determined bottom roughnesses are used in conjunction with the eddy viscosity model, predictions of attenuation for individual wave components closely match measurements. When the wave boundary layer thickness is defined to be the height at which the predicted velocity deficit in the wave boundary layer is within 5% of the free stream velocity, excellent agreement is obtained between predicted and measured velocity profiles for currents in the presence of codirectional waves. Therefore these experiments show that a single bottom roughness, when used in conjunction with an equivalent wave representation, adequately characterizes both monochromatic and spectral wave-current boundary layer flows over a fixed rippled bed. IntroductionFluid velocities in bottom boundary layers play a significant role in defining circulation and sediment transport in coastal regions. Accordingly, numerous investigators have developed models to predict velocity distributions in bottom boundary layers for waves and currents. The most widely used models achieve turbulence closure using an eddy viscosity because of the simplicity and utility of this approach. To scale the eddy viscosity near the bottom, most eddy viscosity models use a time-invariant shear velocity for a velocity scale and the distance from the bed for the length scale. Examples of these eddy viscosity models include the models of Lundgren [1972] [1985], and Grant and Madsen [1979, 1986]. In particular, the model of Grant and Madsen [1979, 1986]

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A Parametric Wind Wave Model for Arbitrary Water Depths

Cited by 3 publications

References 78 publications

Turbulent boundary layers under irregular waves and currents: Experiments and the equivalent‐wave concept

Turbulent boundary layers under irregular waves and currents: Experiments and the equivalent‐wave concept

A Simple Model for Random Wave Bottom Friction and Dissipation

Waves and currents over a fixed rippled bed: 3. Bottom and apparent roughness for spectral waves and currents

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