Numerical Investigation of the Energy Transfer in a Coupled Wind and Wave SystemWilliam Xuanting Hao (), Lian ShenSt. Anthony Falls Lab & Dept. Mechanical EngineeringUniversity of MinnesotaAPS 69th Annual DFD Meeting, Portland, OR, Nov., 2016

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Background Phase-Averaged Wave Model

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Nonlinear wave interaction dominant over wind input / dissipation.Background Dominant Processes in Wind-Wave Growth

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Conduct high-fidelity numerical experiments for a coupled wind-wave system with turbulence over irregular wave fields

Quantify the key energy transfer processes in wind-wave interaction

Investigate the role of nonlinear interaction in long-term wave evolution based on quantitative analysis.Objective

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LES of atmospheric turbulence on wave-surface-fitted grid to capture the real geometry of waveTwo-way coupling between wind and dynamically-evolving nonlinear wavesFractional step scheme for time integrationProjection method for mass conservation

Wind and wave evolution with two-way couplingwind forcingwave geometry and velocity

Yang & Shen (JCP, 2011)Wind over Waves with Dynamic Two-Way Coupling

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Initial wave field constructed using JONSWAP spectrumModerate wind speed to reduce wave breaking effectRepresentative wave ages in the intermediate range Problem Setup

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Turbulence over WavesMean streamwise velocity yielding the log law of the wallReynolds shear stress similar to flows past a flat plate. Wave effect indistinguishable.

Reynolds shear stress as a function of the vertical heightMean profile of the streamwise velocity

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Turbulence over WavesQuadrant ratio in the under-developed region and reasonably consistent with results in the literature.Quadrant ratio as a function of the wave ageQuadrant ratio (Sullivan et al. JAS 2008)

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Wave StatisticsSkewness and kurtosis as a function of time for case ww7

GaussianG-C seriesPresent studyPDF

PDF of the normalized surface elevation at a time instant

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Kinetic equation for the four-wave interaction: (Hasselmann, JFM, 1962, 1963)

QuadratureWRTPresent studyEvaluating the nonlinear interaction term numericallyValidated for the wave field (no wind input)Compared with the exact solution using the quadrature method (Lavrenov, JPO, 2001) and the WRT method (Webb, Deep Sea Research, 1978; Tracy & Resio, Tech Report,1982)Overall consistency, with deviation and oscillation caused by interpolation and resolutionNormalized nonlinear interaction term in the omnidirectional form Nonlinear Wave-Wave Interaction without Wind

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Nonlinear Wave-Wave Interaction Under Wind

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Definition of the wave growth rate:

Liu, Yang, Guo & Shen (PoF, 2010)A sketch of monochromatic wave and the wave-induced pressureQuantifying the Wind Input

Wave growth rate as a function of wave age

Quantifying the Wind Input

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Quantifying the Wind Input

Wave growth rate as a function of steepness

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indicates the direction of time increase

Wave Field EvolutionFrequency downshift observed for all casesNormalized wave spectrum at different time

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Wave Field EvolutionWave growth constant as a function of the normalized peak frequency

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ConclusionsThis presentation was made possible, in part, through financial support from the Council of Graduate Students at University of Minnesota.

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Thanks!Questions?