A new evaluation of the wind stress coefficient over water surfaces

Amorocho, J.; DeVries, Johannes J.

doi:10.1029/jc085ic01p00433

Cited by 195 publications

(105 citation statements)

References 16 publications

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“…The model also includes a filter to control the numerical diffusion of potential energy (Laval et al 2003a), so the stratification and the phase speed of the internal waves are not altered numerically over the simulation period. Heat and momentum exchange at the water surface was estimated by bulk transfer models (e.g., Amorocho and DeVries 1980;Imberger and Patterson 1981;Jacquet 1983), the transfer coefficient being corrected for the stability of the atmospheric boundary layer (Hicks 1975). The surface-energy fluxes are separated into a nonpenetrating component introduced in the surface mixed layer, and a penetrating component introduced over one or more layers according to Beer's law.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

2006

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Field data and numerical simulations were used to investigate the effects of basin shape, continuous stratification, and rotation on the three-dimensional structure of the dominant natural basin-scale internal-wave modes in Lake Kinneret, a stratified lake large enough so that the earth's rotation influences the wave motion. The structure of the modes was inferred from power spectral density of measured and simulated isotherm vertical displacements and from rotary-power spectral density of isopycnal velocities obtained from numerical simulations. The shape of the lake at the level of the thermocline, in conjunction with the dispersion relationship, determines the horizontal configuration of the natural modes. The dominant response to wind forcing was an azimuthal and vertical mode 1 Kelvin wave with a natural period of 22.6 h that propagated around the entire basin; the second most dominant response was a vertical mode 1 wave with a natural period close to 10.5 h and composed of two counter-rotating Poincaré circular cells. The sloping bottom produced an intensification of vertical displacements and velocities over the slope due to focusing of waves rays after reflection at bottom slopes close to the critical angle. The amplitude of the observed oscillations was very sensitive to the phase of the wind relative to the existing waves; resonance was affected by the cessation time of the wind events because it defines the local forcing period and resets the phase of the observed oscillations.

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Section: Numerical Simulationsmentioning

confidence: 99%

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

2006

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“…PAR, photosynthetically active radiation; NIR, near infrared radiation; UVA, ultraviolet A (long wave) radiation; UVB, ultraviolet B (medium wave) radiation. (Amorocho and de Vries 1980) as r air c 10 (w 10 ) 2 , where c 10 is the drag coefficient and w 10 is the wind speed at 10-m altitude. The power (W) transferred into the seiche motion by wind was described by aA 0 r air c 10 |w 10 | 3 , with the coefficient a given in Table 3.…”

Section: Methodsmentioning

confidence: 99%

“…The seiche energy, E seiche , is an internal AQUASIM parameter and was calculated by the program at each iteration step at all depth levels. For dissipation e (W kg 21 ) of turbulent kinetic energy (TKE), the rate of e production (W kg 21 s 21 ) within the water column was described by a standard k-e model expression (Amorocho and de Vries 1980): c 1 (P + c 3 G)(e/k) 2 c 2 (e 2 /k). Here, k (J kg 21 ) is the turbulent kinetic energy (TKE) per unit mass of water, P (W kg 21 ) is the production of TKE due to shear of horizontal velocity, and G (W kg 21 ) is the production or loss of TKE due to density differences.…”

Section: Methodsmentioning

confidence: 99%

Mixing and its effects on biogeochemistry in the persistently stratified, deep, tropical Lake Matano, Indonesia

Katsev

Crowe

Mucci

et al. 2010

Limnology & Oceanography

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In the . 590-m deep, tropical Lake Matano (Indonesia), stratification is characterized by weak thermal gradients (, 2uC per 500 m) and weak salinity gradients (, 0.14% per 500 m). These gradients persist over seasons, decades, and possibly centuries. Under these nearly steady-state conditions, vertical eddy diffusion coefficients (K z ) cannot be estimated by conventional methods that rely on time derivatives of temperature distributions. We use and compare several alternative methods: one-dimensional k-e modeling, three-dimensional hydrodynamic modeling, correlation with the size of Thorpe instabilities, and correlation with the stability frequency. In the thermocline region, at 100-m depth, the K z is , 5 3 10 26 m 2 s 21 , but, below 300 m, the small density gradient results in large (20 m) vertical eddies and high mixing rates (K z , 10 22 m 2 s 21 ). The estimated timescale of water renewal in the monimolimnion is several hundred years. Intense evaporation depletes the surface mixed layer of 16 O and 1 H isotopes, making it isotopically heavier. The lake waters become progressively isotopically lighter with depth, and the isotopic composition in the deep waters is close to those of the ground and tributary waters. The vertical distribution of K z is used in a biogeochemical reaction-transport model. We show that, outside of a narrow thermocline region, the vertical distributions of dissolved oxygen, iron, methane, and phosphorus are shaped by vertical variations in transport rates, rather than by sources or sinks.

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“…Heat exchange through the water's surface is governed by standard bulk transfer models found in the literature (e.g., Amorocho and DeVries 1980;Imberger and Patterson 1981;Jacquet 1983). The energy transfer across the free surface is separated into nonpenetrative components of long-wave radiation, sensible heat transfer, and evaporative heat loss, complemented by penetrative shortwave radiation.…”

Section: Methodsmentioning

confidence: 99%

Modeling basin‐scale internal waves in a stratified lake

Hodges

Imberger

Saggio

et al. 2000

Limnology & Oceanography

347

288

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Basin-scale internal waves provide the driving forces for vertical and horizontal fluxes in a stratified lake below the wind-mixed layer. Thus, correct modeling of lake mixing and transport requires accurate modeling of basinscale internal waves: examining this capability with a hydrostatic, z-coordinate three-dimensional (3D) numerical model at coarse grid resolutions is the focus of this paper. It is demonstrated that capturing the correct thermocline forcing with a 3D mixed-layer model for surface dynamics results in a good representation of low-frequency internal wave dynamics. The 3D estuary and lake computer model ELCOM is applied to modeling Lake Kinneret, Israel, and is compared with field data under summer stratification conditions to identify and illustrate the spatial structure of the lowest-mode basin-scale Kelvin and Poincaré waves that provide the largest two peaks in the internal wave energy spectra. The model solves the unsteady Reynolds-averaged Navier-Stokes equations using a semi-implicit method similar to the momentum solution in the TRIM code with the addition of quadratic Euler-Lagrange discretization, scalar (e.g., temperature) transport using a conservative flux-limited approach, and elimination of vertical diffusion terms in the governing equations. A detailed description is provided of turbulence closure for the vertical Reynolds stress terms and vertical turbulent transport using a 3D mixed-layer model parameterized on wind and shear energy fluxes instead of the convential eddy viscosity/diffusivity assumption. This approach gives a good representation of the depth of the mixed-layer at coarse vertical grid resolutions that allows the internal waves to be energized correctly at the basin scale.Wind stresses, surface heating, and density currents form the driving energy fluxes of a stratified lake. The basin-scale energy flux from the wind is of particular interest because of its dominant role in setting the thermocline in motion, which, in the absence of inflows and outflows, is the primary energy store for transport and mixing below the wind-mixed layer. Thus, modeling the basin-scale internal wave behavior is an a priori requirement to modeling and quantifying the flux paths of nutrients in a stratified lake (Imberger 1994). This paper takes a first step in this direction by analyzing our ability to model basin-scale internal waves that are seen in Lake Kinneret, Israel.Energy flux path in a stratified lake-Energy flux through a stratified lake has a fundamental dependence on forced and free baroclinic motions. The wind imparts both momentum and turbulent kinetic energy (TKE) to the water in the surface layer. The TKE distributes momentum vertically in the 1 Corresponding author

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A new evaluation of the wind stress coefficient over water surfaces

Cited by 195 publications

References 16 publications

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

Mixing and its effects on biogeochemistry in the persistently stratified, deep, tropical Lake Matano, Indonesia

Modeling basin‐scale internal waves in a stratified lake

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