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The bursting sequence in the turbulent boundary layer over progressive, mechanically generated water waves

Published online by Cambridge University Press:  21 April 2006

Yiannis Alex Papadimitrakis ,
Robert L. Street  and
En Yun Hsu
Yiannis Alex Papadimitrakis
Affiliation:
Goddard Space Flight Center, Code 671, Greenbelt, MD 20771, USA
Robert L. Street
Affiliation:
Environmental Fluid Mechanics Laboratory, Department of Civil Engineering, Stanford University, Stanford, CA 94305, USA
En Yun Hsu
Affiliation:
Environmental Fluid Mechanics Laboratory, Department of Civil Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

The structure of the pressure and velocity field in the air above progressive, mechanically generated water waves was investigated in order to evaluate the influence of a mobile and deformable boundary on turbulence production and the related bursting phenomena. The Reynolds stress fluctuations were measured in a transformed Eulerian wave-following frame of reference, in a wind-wave research facility at Stanford University.

The structure of the wave-coherent velocity field was found to be very sensitive to the height of the critical layer below which the waves travel faster than the wind. Because the critical-layer height changes rapidly with the ratio (c / u*) of the wave speed to the wind friction velocity, the structure of the wave-coherent velocities depends strongly on the parameter c/Uδ0, where Uδ0 is the mean free-stream wind velocity. When the critical height is large enough that most of the flow in the turbulent boundary layer is below the critical height, the structure of the wave-coherent velocities is strongly affected by the Stokes layer (in the air), which under the influence of turbulence can have thickness comparable with the wave amplitude. In contrast, when the critical height is small enough that most of the flow in the boundary layer is above the critical height, the structure of the wave-coherent velocities is strongly affected by the critical layer. The latter was found to be nonlinear and turbulently diffusive.

The dependence of the structural behaviour of the wave-coherent velocity field upon the critical and Stokes layers results in considerable modifications of the turbulence-generating mechanism during the bursting-cycle, as the dimensionless wave speed c/Uδ0 changes. Such modifications are manifested by an enhancement of the contributions to the mean Reynolds stress of the bursting events (relative to their solid-wall counterparts), and their dependence on the dimensionless wave speed. For c/Uδ0 [ges ] 0.68 (or c/u* > 20), the nonlinear critical-layer thickness is large compared to the wave amplitude (except when c/Uδ0 = 0.68), and the diffused Stokes layer stimulates the wave-associated stress production. In the water proximity, the bursting contributions remain nearly constant with dimensionless wave speed; ejections account for 90% of the mean Reynolds stress, whereas sweeps provide 77%, the excess over 100% being balanced by the outward and inward interactions. For c/Uδ0 < 0.68, the critical-layer thickness is smaller than the wave amplitude and all contributions increase gradually with c/Uao. However, the ratio of ejection to sweep contributions remains unaltered and ≈ 1.15, indicating that sweeps are nearly as energetic as ejections a t all dimensionless wave speeds. The value of c/Uδ0 ≈ 0.68 appears to separate the flow regimes of high and low critical level, respectively, where significant and weak production of the wave-associated stresses have been found. Near the water surface the height distribution of the fractional contributions of the bursting events is also sensitive to the ratio c/UJO. In the equilibrium region of the boundary layer it remains uniform and in the free stream rises sharply, independent of dimensionless wave speed.

The mean time period between ejections or sweeps depends on both the wave and wind field characteristics and does not scale with either the inner or the outer flow variables. The former can be determined from the time between the first two largest consecutive peaks of the phase-averaged Reynolds stress distribution.

In the water proximity, the height distribution of the normalized energy production is sensitive to c/Uδ0; only when c/Uδ0 [ges ] 0.68 does it show a peak of increasing magnitude with increasing dimensionless wave speed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 303 - 345
Copyright
© 1988 Cambridge University Press

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