En Yun Hsu

Direct measurement of aerodynamic pressure above a simple progressive gravity wave

Measurements of the aerodynamic pressure distribution at the interface between air and simple progressive water waves are obtained with the use of a pressure sensor that follows the water surface. The theory of Miles (1957, 1959) and Benjamin (1959) on shear flows past a wavy boundary predicts a phase shift between the pressure distribution along the boundary and the boundary itself. An experimental verification of this theory is sought especially. A wind–wave facility 115 ft. long, 6 ft. high and 3 ft. wide was used. The facility is equipped with an oscil-lating-plate wave-generator which is capable of generating sinusoidal or arbitrary wave-forms, and a suction fan which can produce wind velocities up to 80 ft./sec when the water is at a nominal depth of 3 ft. The pressure sensor used for the measurements of pressure, was mounted on an oscillating device such that the sensor could be maintained at a fixed small distance (within 1/4 in.) above a propagating wavy surface at all times. The perturbation pressure over progressive waves is extracted from recorded data sensed by the moving sensor. The results compare favourably with the theoretical predictions of Miles (1959).

The role of wave-induced pressure fluctuations in the transfer processes across an air−water interface

The structure of the pressure and velocity fields in the air above mechanically generated water waves was investigated in order to evaluate their contribution to the transfer of momentum and energy from wind to water waves. The measurements were taken in a transformed Eulerian wave-following frame of reference, in a wind-wave research facility at Stanford University. The organized component of the fluctuating static pressure at the channel roof was found to contain contributions from both the sound field and the reflected water wave. The acoustic contributions were accounted for by appropriately correcting the pressure amplitude and phase (relative to the wave) and its contribution to the momentum and energy exchange. The wave-induced pressure coefficient at the fundamental mode shows in general an exponential decay behaviour with height, but the rate of decay is different from that predicted by potential-flow theory. The wave-induced pressure phase relative to the wave remains fairly constant throughout the boundary layer, except when the ratio of the wave speed to the freestream velocity, c / U δ0 = 0.78 and 0.68. This phase difference was found to be about 130° during active wave generation, with the pressure lagging the wave. The momentum and energy transfer rates supported by the waves were found to be dominated by the wave-induced pressure, but the transfer of the corresponding total quantities to both waves and currents may or may not be so dominated, depending on the ratio c / U δ0 . The direct contribution of the wave-induced Reynolds stresses to the transfer processes is negligible.

THE BURSTING SEQUENCE IN THE TURBULENT BOUNDARY LAYER OVER PROGRESSIVE, MECHANICALLY GENERATED WATER WAVES

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 / U δ 0 , where U δ 0 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 / U δ 0 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 / U δ 0 [ges ] 0.68 (or c / u * > 20), the nonlinear critical-layer thickness is large compared to the wave amplitude (except when c / U δ 0 = 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 / U δ 0 c / U δ 0 ≈ 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 / U δ 0 ; only when c / U δ 0 [ges ] 0.68 does it show a peak of increasing magnitude with increasing dimensionless wave speed.

On the Structure of the Velocity Field over Progressive Mechanically-Generated Water Waves

Abstract The structure of the velocity field over a propagating wave of fixed frequency is examined. The vertical and horizontal velocities were measured in a transformed Eulerian wave-following frame of reference in a wind-wave research facility at Stanford University. Experimental results are given for seven different wind speeds in the range 140–402 cm s−1, with 1 Hz, 2.54 cm nominal amplitude, mechanically-generated sinusoidal water waves. The mean velocity profiles have a log-linear form with a wake free-stream characteristic. The constant C which characterizes these profiles decreases with increasing wind speed, as a result of the variation of surface roughness condition between the transition region and the fully rough regime. The wave-associated stresses with their main component at twice the fundamental wave frequency were found to be significant. Therefore, the nonlinear terms encountered in the wave-induced Navier-Stokes equations associated with these stresses cannot be neglected, and lineariz...

On the resolution of organized spurious pressure fluctuations in wind–wave facilities

The structure of the fluctuating wall pressure beneath a turbulent boundary layer influenced by the presence of progressive, mechanically generated water waves of fixed frequency is examined. This pressure was measured by an array of five piezocrystal pressure transducers mounted on the roof of a wind–wave research facility at Stanford University. Experimental results are given for seven wind speeds in the range 1.4–4.0 m/s, with 1‐Hz, 2.54‐cm nominal amplitude, sinusoidal water waves. The organized component of the wall pressure was found to be contaminated by an acoustic plane and other pressure waves associated with the traveling upstream‐reflected water wave. The spurious pressure components are an order of magnitude greater than, and comparable to the traveling downstream wave‐induced pressure at the channel roof. The turbulent static pressure fluctuations contain sound contributions in the form of narrow‐band noise. The resolution of the various components of the organized wall pressure was achieved...

Measurements of the Fluctuating Pressure in the Turbulent Boundary Layer over Progressive, Mechanically Generated Water Waves

The structure of pressure and velocity fields in the air above mechanically generated water waves was investigated in order to evaluate their contribution to the transfer of momentum and energy from wind to water waves. The wave-induced composite pressure coefficient, at the fundamental mode, shows in general an exponential decay behavior, but the rate of decay is different from that predicted by potential flow theory. The relative wave-induced pressure phase remains fairly constant throughout the boundary layer. The momentum and energy transfer rates supported by the waves were found to be dominated by the wave-induced pressure, but the transfer of the corresponding total quantities to both waves and current may or may not, depending on the ratio of the wave speed to the free-stream velocity, c/U. The contribution of the wave-induced Reynolds stresses to the transfer processes is negligible.

DYNAMICS OF WIND IN THE VICINITY OF PROGRESSIVE WAVES

INTRODUCTION For the design of a coastal structure, the height of its crown must be determined rationally and economically, taking into consideration the water level of the sea and its occurence probability. The water level in the sea is mainly referred to the astronomical tide, the meteorological effect and the short period wave. If component height according to these elements are given as; 3c, ; the tidal level, xr ; the level rise caused by meteorological origin, and x, ; the half height of wave, the level of the wave crest X at a certain tidal condition is shown by following equation under several assumption: I a i + X, + X, (1)