Stably stratified airflow over a waved water surface. Part 1: Stationary turbulence regime

Druzhinin, O. A.; Troitskaya, Yuliya; Zilitinkevich, Sergej

doi:10.1002/qj.2677

Cited by 22 publications

(26 citation statements)

References 34 publications

(58 reference statements)

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“…A detailed derivation of the momentum‐flux balance in the unladen‐flow case (rewritten in curvilinear, wave‐following coordinates) can be found in, e.g., Druzhinin et al . []. In a two‐way‐coupled situation, a momentum‐flux source due to drops is added to the total momentum‐flux balance [ Richter and Sullivan , ].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Thus in this case, the resulting momentum‐flux balance equation can be written in the following form [cf. Druzhinin et al ., ]:

true[ν \frac{\partial true〈 U_{x} true〉}{\partial η} + \frac{\partial z}{\partial ξ} false〈 U_{x}^{2} + \frac{P}{ρ_{a}} false〉 - \frac{\partial z}{\partial η} true〈 U_{x} U_{z} true〉 + \int_{0}^{η} J false(ξ, η false) 〈 f_{x} 〉 d η true] + τ_{d 0} = τ_{t o t a l},

where

τ_{d 0}

is a uniform constant to be defined below, and

τ_{t o t a l}

is the total stress. In the statistically stationary flow‐state,

τ_{t o t a l}

is a uniform constant.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The left‐hand side of equation can be rewritten as a sum of the viscous stress

τ_{v}

, the wave‐induced air‐momentum flux (including the form stress)

τ_{w}

, the turbulent air‐momentum flux

τ

, and the stress contribution due to the feedback force by the drops

τ_{d}

τ_{v} + τ_{w}^{} + τ + τ_{d} = τ_{t o t a l},

where the viscous stress is

τ_{v} = ν \frac{d true[true〈 U_{x} true〉 true]}{d η},

the wave‐induced momentum flux is evaluated as [ Druzhinin et al ., ]

τ_{w} = true[\frac{\partial z}{\partial ξ} true〈 U_{x}^{2} + P true〉 - true(\frac{\partial z}{\partial η} - 1 true) true〈 U_{x} U_{z} true〉 - true〈 U_{x} true〉 true〈 U_{z} true〉 true],

the turbulent momentum flux

τ

is given by (22).…”

Section: Numerical Resultsmentioning

confidence: 99%

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The study of droplet‐laden turbulent airflow over waved water surface by direct numerical simulation

2017

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The objective of the present paper is to elucidate possible effects of sea spray on the momentum transfer in marine boundary layer under strong wind forcing conditions by performing direct numerical simulation (DNS) of turbulent, droplet‐laden airflow over a waved water surface. Three‐dimensional, turbulent Couette airflow is considered in DNS as a model of a constant‐flux layer in the atmospheric surface layer. Two‐dimensional stationary waves at the water surface are prescribed and assumed to be unaffected by the airflow and/or droplets. Droplets are considered as nondeformable spheres and tracked in a Lagrangian framework, and their impact on the carrier flow is modeled with the use of a point‐force approximation. The results show that drops dynamics and their impact on the carrier airflow is controlled by the drops velocity at injection, the ratio of drops gravitational settling velocity versus the product of air friction velocity and Karman constant ( Vg/κu∗), and the wave slope, ka. Drops injected into the flow with the surrounding airflow velocity reduce the turbulent air‐stress and increase mean air velocity as compared to the droplet‐free case. On the other hand, the opposite effect is observed for drops injected with velocity equal to the water surface velocity, which increase the turbulent air stress and reduce the mean wind velocity. This modification of the airflow by drops is most pronounced for the ratio Vg/κu∗≈1, increases with drops mass loading, and is reduced for steeper waves and smaller settling velocity.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Thus in this case, the resulting momentum‐flux balance equation can be written in the following form [cf. Druzhinin et al ., ]:

true[ν \frac{\partial true〈 U_{x} true〉}{\partial η} + \frac{\partial z}{\partial ξ} false〈 U_{x}^{2} + \frac{P}{ρ_{a}} false〉 - \frac{\partial z}{\partial η} true〈 U_{x} U_{z} true〉 + \int_{0}^{η} J false(ξ, η false) 〈 f_{x} 〉 d η true] + τ_{d 0} = τ_{t o t a l},

where

τ_{d 0}

is a uniform constant to be defined below, and

τ_{t o t a l}

is the total stress. In the statistically stationary flow‐state,

τ_{t o t a l}

is a uniform constant.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The left‐hand side of equation can be rewritten as a sum of the viscous stress

τ_{v}

, the wave‐induced air‐momentum flux (including the form stress)

τ_{w}

, the turbulent air‐momentum flux

τ

, and the stress contribution due to the feedback force by the drops

τ_{d}

τ_{v} + τ_{w}^{} + τ + τ_{d} = τ_{t o t a l},

where the viscous stress is

τ_{v} = ν \frac{d true[true〈 U_{x} true〉 true]}{d η},

the wave‐induced momentum flux is evaluated as [ Druzhinin et al ., ]

τ_{w} = true[\frac{\partial z}{\partial ξ} true〈 U_{x}^{2} + P true〉 - true(\frac{\partial z}{\partial η} - 1 true) true〈 U_{x} U_{z} true〉 - true〈 U_{x} true〉 true〈 U_{z} true〉 true],

the turbulent momentum flux

τ

is given by (22).…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The study of droplet‐laden turbulent airflow over waved water surface by direct numerical simulation

2017

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“…According to [3] Pr t was assumed to be 0.85. This value was also confirmed by direct numerical simulation of turbulent boundary layer above waved water surface [26]. To determine the constants D Ɍ and E Ɍ data processing was carried out as described above for the velocity profile.…”

Section: The Determination Of Heat and Momentum Flows On The Velocitymentioning

confidence: 55%

“…Three-dimensional spacetime spectra were obtained from the measured data by the algorithm FDM (Fourier Directional Method) [22], similar to Wavelet Directional Method (WDM), suggested in [27]. Then, the three-dimensional space-time spectrum , , S k Z T can be obtained similar to [26] by using the conditional averaging of the spectral amplitudes by k andT .…”

Section: Measuring Parameters Of Surface Wavesmentioning

confidence: 99%

Laboratory modelling of the transfer processes between the ocean and atmosphere in the boundary layers

et al. 2017

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Abstract. The processes of momentum and heat transfer between ocean and atmosphere in the boundary layer were investigated within laboratory modeling for a wide range of wind speed and surface wave including hurricane conditions. Experiments were carried out on the Wind-Wave Flume of the Large Thermostratified Tank of IAP RAS. A special net located under the surface at different depths allows to vary parameters of surface waves independently on wind parameters. Theory of self-similarity of air flow parameters in the flume was used to calculate values aerodynamic and heat transfer coefficients from the measured velocity and temperature profiles by Pito and hotfilm gauges respectively. Simultaneous measurements of surface elevation with system wire allow to obtain spectra and integral parameters of waves. It was demonstrated that in contrast to the drag coefficient, heat transfer coefficient is virtually independent of wind speed and wave parameters to the moment of the beginning of spray generation and then increases rapidly.

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A Laboratory Study of the Effect of Surface Waves on Heat and Momentum Transfer at High Wind Speeds

Troitskaya

Sergeev²,

Vdovin

et al. 2020

Preprint

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Stably stratified airflow over a waved water surface. Part 1: Stationary turbulence regime

Cited by 22 publications

References 34 publications

The study of droplet‐laden turbulent airflow over waved water surface by direct numerical simulation

The study of droplet‐laden turbulent airflow over waved water surface by direct numerical simulation

Laboratory modelling of the transfer processes between the ocean and atmosphere in the boundary layers

A Laboratory Study of the Effect of Surface Waves on Heat and Momentum Transfer at High Wind Speeds

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