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Modeling of the eddy viscosity by breaking waves

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Acta Oceanologica Sinica 2007年第6期26卷 116-123页

作者： ZHANG Shuwen YUAN Yeli ZHENG Quan＇ an South China Sea Environmental Institute Guangdong Ocean University Zhanjiang 524088 China Key Laboratory of Marine Science and Numerical Modeling of State Oceanic Administration First Institute of Oceanography State Oceanic Administration Qingdao 266061 China Department of Meteorology Maryland University Maryland 20742 USA

Breaking wave induced nearsurface turbulence has important consequences for many physical and biochemical processes including water column and nutrients mixing, heat and gases exchange across air-sea interface. The energy loss from wave breaking and the bubble plume penetration depth are estimated. As a consequence, the vertical distribution of the turbulent kinetic energy （TKE）, the TKE dissipation rate and the eddy viscosity induced by wave breaking are also provided. It is indicated that model results are found to be consistent with the observational evidence that most TKE generated by wave breaking is lost within a depth of a few meters near the sea surface. High turbulence level with intensities of eddy viscosity induced by breaking is nearly four orders larger than vw1（ = κu ＊wz）, the value predicted for the wall layer scaling close to the surface, where u ＊w is the friction velocity in water, κ with 0. 4 is the yon Kármán constant, and z is the water depth, and the strength of the eddy viscosity depends both on wind speed and sea state, and decays rapidly through the depth. This leads to the conclusion that the breaking wave induced vertical mixing is mainly limited to the near surface layer, well above the classical values expected from the similarity theory. Deeper down, however, the effects of wave breaking on the vertical mixing become less important.

关键词： air-sea interface near-surface dynamics TKE dissipation rate eddy viscosity

Estimation of eddy viscosity on the South China Sea shelf with adjoint assimilation method

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Acta Oceanologica Sinica 2009年第5期28卷 9-16页

作者： ZHANG Yanwei TIAN Jiwei XIE Lingling Physical Oceanography Laboratory Ocean University of China Qingdao 266003 China

The eddy viscosity of the ocean is an important parameter indicating the small-scale mixing process in the oceanic interior water column. Ekman wind-driven current model and adjoint assimilation technique are used to calculate the vertical profiles of eddy viscosity by fitting model results to the observation data. The data used in the paper include observed wind data and ADCP data obtained at Wenchang Oil Rig on the SCS （the South China Sea） shelf in August 2002. Different simulations under different wind conditions are analyzed to explore how the eddy viscosity develops with varying wind field. The results show that the eddy viscosity endured gradual variations in the range of 10^-3 -10^-2 m^2 /s during the periods of wind changes. The mean eddy viscosity undergoing strong wind could rise by about 25% as compared to the value under weak wind.

关键词： the SCS eddy viscosity near-inertial Ekman Model adjoint assimilation

Dynamic modeling of the horizontal eddy viscosity coefficient for quasigeostrophic ocean circulation problems

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Journal of Ocean Engineering and Science 2016年第4期1卷 300-324页

作者： Romit Maulik Omer San School of Mechanical and Aerospace Engineering Oklahoma State UniversityStillwaterOK 74078USA

This paper puts forth a simplified dynamic modeling strategy for the eddy viscosity coefficient parameterized in space and *** eddy viscosity coefficient is dynamically adjusted to the local structure of the flow using two different nonlinear eddy viscosity functional forms to capture anisotropic dissipation mechanism,namely,(i)the Smagorinsky model using the local strain rate field,and(ii)the Leith model using the gradient of the vorticity *** proposed models are applied to the one-layer and two-layer wind-driven quasigeostrophic ocean circulation problems,which are standard prototypes of more realistic ocean *** show that both models capture the quasi-stationary ocean dynamics and provide the physical level of eddy viscosity distribution without using any a priori ***,it is found that slightly less dissipative results can be obtained by using the dynamic Leith ***-layer numerical experiments also reveal that the proposed dynamic models automatically parameterize the subgrid-scale stress terms in each active ***,the proposed scale-aware models dynamically provide higher values of the eddy viscosity for smaller resolutions taking into account the local resolved flow information,and addressing the intimate relationship between the eddy viscosity coefficients and the numerical resolution employed by the quasigeostrophic models.

关键词： eddy viscosity Dynamic Smagorinsky model Dynamic Leith model Anisotropic dissipation One-layer problem Two-layer problem

A Simple eddy viscosity Model of Rough Turbulent Wave Boundary Layer

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China Ocean Engineering 1996年第3期11卷 281-294页

作者： Hsu Tai-Wen and Lin Hwung-Yui Associate Professor, Department of Hydraulics and Ocean Engineering, National Cheng Kung University, Tainan Graduate student, Department of Hydraulics and Ocean Engineering, National Cheng Kung University, Tainan Dept. of Hydr. and Ocean Engineering National Cheng Kung University Tainan Taiwan

A one-layer time-invariant eddy viscosity model is specified to develop a mathematical model for describing the essential features of the turbulent wave boundary layer over a rough bed. The functional form of the eddy viscosity is evaluated based on computational results from a two-equation turbulence model in which the eddy viscosity varies with time and space. The present eddy viscosity model simplifies much of the mathematical complexity in many existing models. Predictions from the present model have been compared with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.

关键词： turbulent wave boundary layer eddy viscosity wave fiction factor

Modeling of the eddy viscosity by breaking waves

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Modeling of the eddy viscosity by breaking waves

Tide-Induced Mixing in the Bottom Boundary Layer in the Western East China Sea

全国计算机物理学会第六届年会和学术交流会

作者： Zhang Shuwen South China Sea Environmental Institute,Guangdong Ocean University,Zhanjiang 524088,China

Wave breaking induced the near-surface turbulence has important consequences for many physical and biochemical processes including water column and nutrients mixing,heat and gases exchange across air-sea *** energy loss from wave breaking and the bubble plume penetration depth are estimated in this *** a consequence,the vertical distribution of the turbulent kinetic energy (TKE),the TKE dissipation rate and the eddy viscosity induced by wave breaking are also *** is indicated that our model results are found to be consistent with the observational evidence that most TKE generated by wave breaking is lost within a depth of a few meters near the sea *** turbulence levels with intensities of eddy viscosity induced by breaking is nearly four orders larger than V

关键词： Wave breaking TKE dissipation rate eddy viscosity

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Journal of Ocean University of China 2023年第1期22卷 1-8页

作者： GUO Zheng CAO Anzhou WANG Jianfeng Marine Science and Technology College Zhejiang Ocean UniversityZhoushan 316022China Ocean College Zhejiang UniversityZhoushan 316021China Institute of Oceanology Chinese Academy of SciencesQingdao 266071China Center for Ocean Mega-Science Chinese Academy of SciencesQingdao 266071China

The East China Sea(ECS)boasts a vast continental shelf,where strong tidal motions play an important role in the substance transport and energy *** this study,the tide-induced mixing in the bottom boundary layer in the western ECS is analyzed based on records measured by moored acoustic Doppler current profilers from June to October *** show that the M_(2) tide is strong and shows a barotropic feature,whereas the O_(1) tide is much *** on the M_(2) tidal currents,the eddy viscosity in the bottom Ekman boundary layer is estimated with three *** estimated eddy viscosity values vary within 10^(-4)–10^(-2)m^(2) s^(−1),reaching a maximum at approximately 5 m height from the bottom and decreasing exponentially with the height at all three ***,the shear production of turbulent kinetic energy is calculated to quantify the mixing induced by different tidal *** results show that the shear production of the M_(2) tide is much stronger than that of the O_(1) tide and shows a bottom intensified feature.

关键词： tides East China Sea bottom boundary layer mixing eddy viscosity

MODIFIED LOG-WAKE LAWS FOR TURBULENT FLOW OF THE OUTER AND INNER REGIONS IN SMOOTH PIPES

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Journal of Hydrodynamics 2007年第2期19卷 188-194页

作者： LIU Ya-kun NI Han-gen State key Laboratory of Coastal and offshore Engineering Dalian University of Technology Dalian 116024 china

Based on theoretical analysis two modified log-wake laws for turbulent flow in smooth pipes are obtained, one is applicable to the outer region and other one to inner region, the new law for the outer region fits the velocity profile measured in smooth pipes by Zagarola very well and the effect of Reynolds number can be taken into consideration, the velocity profile for inner region satisfies the wall boundary conditions ,equals zero at the pipe wall and smoothly joins up with the velocity profile in outer region, the adopted eddy viscosity model is consistent with Laufer＇s, Nunner＇s and Reichardt＇s experimental data.

关键词： turbulent pipe flow eddy viscosity log-wakelaw outer and inner regions

A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow

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Chinese Journal of Aeronautics 2014年第2期27卷 200-209页

作者： Ma Li Lu Lipeng Fang Jian Wang Qiuhui National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics School of Energy and Power Engineering Beihang University

It is of great significance to improve the accuracy of turbulence models in shock-wave/ boundary layer interaction flow. The relationship between the pressure gradient, as well as the shear layer, and the development of turbulent kinetic energy in impinging shock-wave/turbulent bound- ary layer interaction flow at Mach 2.25 is analyzed based on the data of direct numerical simulation （DNS）. It is found that the turbulent kinetic energy is amplified by strong shear in the separation zone and the adverse pressure gradient near the separation point. The pressure gradient was non-dimensionalised with local density, velocity, and viscosity. Spalart Allmaras （S A） model is modified by introducing the non-dimensional pressure gradient into the production term of the eddy viscosity transportation equation. Simulation results show that the production and dissipation of eddy viscosity are strongly enhanced by the modification of S-A model. Compared with DNS and experimental data, the wall pressure and the wall skin friction coefficient as well as the velocity profile of the modified S-A model are obviously improved. Thus it can be concluded that the mod- ification of S-A model with the pressure gradient can improve the predictive accuracy for simulat- ing the shock-wave/turbulent boundary laver interaction.

关键词： eddy viscosity Pressure gradient Shock-wave/turbulentboundary layer interaction Spalart-Allmaras model Turbulent kinetic energytransport property

A Boussinesq Equation-Based Model for Nearshore Wave Breaking

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海洋工程：英文版 2004年第2期18卷 315-320页

作者：余建星张伟王广东杨树清 School of Construction

Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally's analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.

关键词： wave breaking numerical model Boussinesq equation eddy viscosity