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Turbulent structure of air flow over wind-induced gravity waves

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Abstract

This is the second paper in a group of three that reports the systematic measurements of wind-generated water waves in a wind tunnel experiment. Here, the structure of the boundary layer on the air side of the water–air interface was analysed and compared with the boundary layer over a smooth plane rigid wall. The contribution of the wave-induced Reynolds stress was detected through filtering the spectrum of velocity fluctuations. Wave-induced Reynolds stresses became negligible for z > 5 H rms. The intermittency factor in the boundary layer over water waves was similar to that in a boundary layer over a rigid plane wall, with several differences near the interface. Here, the presence/absence of water damps out the turbulence. The quadrant analyses revealed that ejection and sweep events were dominant and more concentrated. At small fetches, the large-amplitude negative streamwise perturbations were preferentially lifted. Turbulence energy production peaked at z/δ = 0.2 and had a distribution similar to that observed for a self-preserving boundary layer with a strong adverse gradient pressure. The quadrant analysis contribution to the energy production revealed that ejections still dominated the balance and that the production was spatially modulated in the wind direction with a couple of cells and with a minimum in the area of the free surface wave height reduction.

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Abbreviations

\( \overline{ \ldots } \) :

Time average operator

\( \widetilde{ \ldots } \) :

Oscillating term operator

\( \widehat{ \ldots } \) :

Phasic average operator

Φ:

Volume fraction or concentration for water

δ :

Boundary layer thickness

γ :

Intermittency factor

ρ :

Mass density

θ :

Angle between wind and wave propagation direction

κ:

Turbulent kinetic energy

ν:

Kinematic fluid viscosity

a :

Exponent

a c :

Crest height

a t :

Trough height

C :

Concentration

c :

Celerity of propagation of the gravity waves

d :

Water depth

H :

Wave height, threshold coefficient

H rms, H mean :

Root mean square wave height, mean wave height

H 1/3 :

Highest one-third wave

k :

Coefficient, von Karman constant

L :

Wave length

p.d.f.:

Probability distribution function

Re, Re x :

Reynolds number, based on the abscissa x

t :

Time

T mean, T 1/3,…:

Period of the waves, mean value, mean value of the first third

TKE:

Turbulent kinetic energy

U :

Streamwise wind velocity

U ∞ :

Asymptotic wind velocity

U 10 :

Wind velocity at the reference level of 10 m

U s :

Drift velocity

U, V :

Streamwise, vertical wind velocity

U′, V′ :

Streamwise, vertical fluctuating wind velocity

u * :

Friction velocity in the air boundary layer

x, y, z, x i :

Spatial co-ordinates

z s :

Instantaneous level of the free surface

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Acknowledgments

The experimental data presented herein were obtained during the author’s sabbatical spent at CEAMA, Grupo de Dinámica de Flujos Ambientales, University of Granada, Spain, kindly hosted by Miguel A. Losada. Financial support from CEAMA is gratefully acknowledged. Special thanks to Luca Chiapponi, Simona Bramato and Christian Mans who provided great help with the experiments.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Parma, Parco Area delle Scienze, 181/A, 43100, Parma, Italy

    Sandro Longo

  2. Centro Andaluz de Medio Ambiente, Universidad de Granada, Avda. del Mediterraneo s/n, 18006, Granada, Spain

    Miguel A. Losada

Authors
  1. Sandro Longo
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  2. Miguel A. Losada
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Correspondence to Sandro Longo.

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Longo, S., Losada, M.A. Turbulent structure of air flow over wind-induced gravity waves. Exp Fluids 53, 369–390 (2012). https://doi.org/10.1007/s00348-012-1294-4

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  • DOI: https://doi.org/10.1007/s00348-012-1294-4

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