A new approach to oscillatory rough turbulent boundary layers

Velocity measurements have been performed in an oscillatory turbulent boundary layer over a rough wall, using a large oscillating water tunnel. These together with measurements by Kalkanis (1964) over an oscillating wall indicate the existence of universal wall and defect laws for velocity. A logarithmic overlap layer is predicted and observed as in a steady turbulent boundary layer, and this results in a new relationship between friction factor and relative boundary layer thickness. The phase lead of the defect velocity relative to the wall ditto seems to follow a universal law over the whole defect layer. A method is suggested for the calculation of the phase lead of wall shear stress over velocity in the free stream for large amplitude to roughness ratios. Apart from the inner layer, it is in principle possible to construct the velocity profiles in a turbulent oscillatory boundary layer at a rough wall, using the findings of this report. A review of experimental and theoretical investigations of the stability of the oscillatory boundary layer is also given.     

A note on a theoretical model of oscillatory smooth turbulent boundary layers

An analytical theory which describes the motion in an oscillatory smooth turbulent boundary layer using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the wall. In the outer layer the eddy viscosity is taken as a constant.     

On the structure of oscillatory boundary layers

An empirical analysis is performed on the most detailed, recent measurements of turbulent oscillatory boundary layer flow. The measurements show that throughout elevations where the flow can be considered horizontally uniform, one deficit model is sufficient for describing the fundamental mode. Some general properties of the non dimensional velocity deficit D₁(z) appear with striking consistency. First of all the identity $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦ ≡}\text{Arg}\text{D}{}_{\mathrm{<mtext>1</mtext>}}$, which is a theoretical result for smooth laminar flow, seems to hold with great accuracy for a large range of turbulent flow conditions as well. This is of principal theoretical interest because all previous analytical eddy viscosity models as well as numerical mixing length models predict a consistent and fairly large difference between Arg D₁ and $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦}$. If the identity between $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦}$ and Arg D₁ extends all the way to the bed, it means that the bed shear stress leads the free stream velocity by 45 degrees. It is also found that the structure of smooth turbulent oscillatory flows as measured by Kalkanis (1964) corresponds to a sharp maximum in the normalized energy dissipation rate.     

Wave boundary layers in rough turbulent flow

A one-layer time-invariant eddy viscosity model is specified to develop a mathematical model for describing the essential features of the turbulent wave boundary layer over a rough bed. The functional form of the eddy viscosity is evaluated based on a modified one-equation turbulence model in which the eddy viscosity varies in time and space. The present eddy viscosity model simplifies much of the mathematical complexity in many existing models. Predictions from the present model have been compared favorably with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.     

A model of oscillatory rough turbulent boundary layer flow

Approximate analytical solutions of the boundary layer equation are obtained in closed form for oscillatory rough turbulent flow. The solutions are based on a time-varying eddy viscosity, and the aim of the study is to assess the effects of these time variations on the properties of the wave boundary layer. The flow and the eddy viscosity are made interdependent by a closure assumption which relates the peak value of viscosity in the wave cycle to the peak value of shear velocity. Instantaneous vertical profiles of horizontal velocity and shear stress, and time series of the bed shear stress, are presented for a typical case study. In addition, the wave drag coefficient, the boundary layer thickness and the phase lead of peak bed shear stress over peak free-stream velocity, are determined as functions of both the relative roughness and the parameter governing the magnitude of the time variations in viscosity. Reasonable agreement is demonstrated with previous experimental and theoretical results.     

Sheet flow and suspension of sand in oscillatory boundary layers

after revisionTime-dependent measurements of flow velocities and sediment concentrations were conducted in a large oscillating water tunnel. The measurements were aimed at the flow and sediment dynamics in and above an oscillatory boundary layer in plane bed and sheet-flow conditions. Two asymmetric waves and one sinusoidal wave were imposed using quartz sand with D₅₀ = 0.21 mm. A new electro-resistance probe with a large resolving power was developed for the measurement of the large sediment concentrations in the sheet-flow layer. The measurements revealed a three layer transport system consisting of a pick-up/deposition layer, an upper sheet flow layer and a suspension layer.In the asymmetric wave cases the total net transport was directed “onshore” and was mainly concentrated in the thin sheet flow layer (< 0.5 cm) at the bed. A small net sediment flux was directed “offhore” in the upper suspension layer. The measured flow velocities, sediment concentrations and sedimenl fluxes showed a good qualitative agreement with the results of a (numerical) 1DV boundary-layer flow and transport model. Although the model did not describe all the observed processes in the sheet-flow and suspension layer, the computational results showed a reasonable agreement with measured net transport rates in a wide range of asymmetric wave conditions.     

Reynolds number variation in oscillatory boundary layers: Part I. Purely oscillatory motion

A numerical model based upon a low Reynolds number turbulence closure is proposed to study Reynolds number variation in reciprocating oscillatory boundary layers. The model is used to compute the boundary layer for flow regimes ranging from smooth laminar to rough turbulent. Criteria for fully developed turbulence are derived for walls of the smooth and rough types. In particular, a new criterion to identify the rough turbulent regime is determined based on the time-averaged turbulence intensity. The reliability of the present model is assessed through comparisons with detailed experimental data collected by other investigators. The model globally improves upon standard high Reynolds number closures. Variation through the wave cycle of the main flow variables (ensemble-averaged velocity, shear stress, turbulent kinetic energy) is remarkably well-predicted for smooth walls. Predictions are satisfactory for rough walls as well. Yet, the turbulence level in the rough turbulent regime is overpredicted in the vicinity of the bed.     

Modelling wave-current interactions in rough turbulent bottom boundary layers

The aim of the present paper is to explain some of the differences between previously published analytical and numerical models of combined wave and current bottom boundary layer flow. To this end, the Grant and Madsen (1979) model for wave-current, rough turbulent flow is modified to include both first and second harmonic time variations in the eddy viscosity (K). The functional form of the coefficients controlling the amount of time variation is established by analysing the numerical model results of Davies (1990). The addition of time variation in K reduces the strong non-linearity exhibited by the mean stress in the original Grant and Madsen model for current dominated cases, and reproduces the veering of the current predicted by numerical turbulence closure models.     

On a theoretical model of rough turbulent wave boundary layers

An analytical theory which describes the motion in a turbulent wave boundary layer near a rough sea bottom by using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the sea bottom. In the outer layer the eddy viscosity is taken as a constant. The mean velocity and shear stress profiles, the bottom shear stress and the bottom friction coefficient are presented, and comparisons are made with experimental results.     

波浪运动在底边界层的湍流结构数值研究

本文基于$ k $-$ \varepsilon $ 模型研究了波流边界层内湍流结构特征。研究结果表明,时均流速分布数值解与实验结果高度吻合。一个波周期内湍流结构特征（如：涡量、湍动能、湍动能耗散率等）呈周期性变化规律,波浪作用引起涡量、湍动能及湍动能耗散率均在减速阶段减小,在波谷处达到最低值,而后在加速阶段增大,并在波峰处达到最大值。近壁面处湍流结构变化幅值较大（湍动能耗散率变化可达53%）,远离壁面处变化幅值较平均值较小（仅3%）。波流边界层厚度在减速阶段增加,在加速阶段减小。本文所建立的数值模型克服了现有模型因采用“高雷诺数方法”引起的近壁区精度不高问题,可较好地描述波浪作用下湍流结构演变过程的物理机制,为河口海岸地区泥沙运动、岸滩演变及海洋可再生能源的开发利用提供一些指导意义。     

A general method for calculating three-dimensional laminar and turbulent boundary layers on ship hulls

A general method for representing the flow properties in the three-dimensional boundary layers around ship hulls of arbitrary shape is described. It makes use of an efficient two-point finite-diffirence schem to solve the boundary-layer equations and includes an algebraic eddy-viscosity representaion of the Reynolds-stress ternsor. The numericzal method contains novel and desirable features and allows the calculation of flows in which the circumferential velocity component contains regions of flow reversal across the boundary layer. The inviscid pressure distribution is determined with the Douglas-Neumann method which, if necessary, can conveniently allow for the boundary-layer displacement surface. To allow its application to ships, and particularly to those with double-elliptic and flat-bottomed hulls, a non-orthogonal coordinate system has been developed and is shown to be economical, precise and comparatively easy to use. Present calculations relate to zero Froude number but they can be extended to include the effects of a water wave and local regions of flow separation which may stem from bulbous-bow geometries.     

An experimental study of turbulent boundary layer with slit suction

Experiments are performed on a flat plate with a transverse suction slit in the Reynolds number range 5 × 10⁵ < R_e < 1.1 × 10⁶. Mean velocity profiles, RMS values are measured with hot wire anemometry. Friction velocity is numerically calculated. The experiments showed that a classical boundary layer parameter α is related to the suction coefficient S_c with an equation of the form: .The value of A seems to depend strongly on the relative location with respect to suction slit and possibly weakly on Reynolds number.     

Fine structure of the turbulent atmospheric boundary layer over the water surface

In this paper, the results of a laboratory experiment on investigating the wind-velocity field over a water surface using the PIV method are described. The use of a rapid CCD-camera made it possible to perform a detailed study of the eddy structure of airflow. We have measured the velocity fields over a flat plate by wind waves and waves induced by a wave generator. The model of a turbulent boundary layer over a rough surface was directly verified. It has been shown that the wind-velocity profiles over waves obtained by averaging the instantaneous fields over the ensemble of samples and horizontal coordinate are satisfactorily consistent with the profiles calculated within the frameworks of the model of wind flow over rough water surface.     

Experimental and theoretical study of a cylindrical oscillating water column device with a quadratic power take-off model

The wave power extraction by a cylindrical oscillating water column (OWC) device with a quadratic power take-off (PTO) model was studied experimentally and theoretically. In the experiment, a scaled model OWC was tested in a wave flume, with an orifice being used to simulate a quadratic PTO mechanism. In the theoretical analysis, the quadratic PTO model was linearized based on Lorenz's principle of equivalent work, which allows us to perform a frequency domain analysis using an eigen-function matching method. The effects of higher harmonic components and the spatial non-uniformity of the surface velocity inside the chamber were discussed. A semi-analytical model was proposed to understand the viscous loss affecting the measured capture length. Our treatment of the quadratic PTO model was validated by comparing quasi-linear theoretical capture length and the laboratory measurement. Our results also showed that the effects of spatial non-uniformity and viscous loss could be noticeable for shorter waves.     

Comparison of theoretical and experimental wall pressure wavenumber-frequency spectra for axisymmetric and flat-plate turbulent boundary layers

The measurement and analysis of turbulent boundary layer wall pressure fluctuations using a wavenumber filter of sensors provide quantitative knowledge of turbulence physics. In addition, the sources of flow-induced noise and vibration for towed SONAR arrays can be determined. An axisymmetric turbulent boundary layer can have significantly different features than those of a comparable flat-plate boundary layer. Here, a detailed comparison of the distribution of wall pressure energy in both wavenumber and frequency between flat-plate and thick axisymmetric boundary layers is presented. The background theory of wavenumber-frequency spectra and state-of-the-art models for flat-plate boundary layers are discussed. The widely used model of Chase (1987), valid for flat-plate boundary layers over a wide range of Reynolds numbers, is used and combined with a sensor response function to allow the effects of spatial averaging to be considered. It is demonstrated that when measured boundary layer parameters for the axisymmetric case are used in the Chase flat-plate model, the results accurately predict the axisymmetric boundary layer wall pressure measurements.     

槽道湍流的展向振荡电磁力壁面减阻

采用直接数值模拟方法,对槽道湍流的展向振荡电磁力的减阻效果和减阻机理进行了研究,讨论了电磁力强度和振荡频率对湍流猝发事件以及壁面减阻率的影响.结果表明,电磁力强度或振荡频率变化时,湍流猝发频率和猝发强度的变化趋势是相反的,所以存在最优参数使得减阻效果最好.等价壁面展向速度可以很好地描述电磁力强度和振荡频率的变化对减阻效果的综合效应.     

Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport

A large number of studies have been done dealing with sinusoidal wave boundary layers in the past. However, ocean waves often have a strong asymmetric shape especially in shallow water, and net of sediment movement occurs. It is envisaged that bottom shear stress and sediment transport behaviors influenced by the effect of asymmetry are different from those in sinusoidal waves. Characteristics of the turbulent boundary layer under breaking waves (saw-tooth) are investigated and described through both laboratory and numerical experiments. A new calculation method for bottom shear stress based on velocity and acceleration terms, theoretical phase difference, φ and the acceleration coefficient, a_c expressing the wave skew-ness effect for saw-tooth waves is proposed. The acceleration coefficient was determined empirically from both experimental and baseline k–ω model results. The new calculation has shown better agreement with the experimental data along a wave cycle for all saw-tooth wave cases compared by other existing methods. It was further applied into sediment transport rate calculation induced by skew waves. Sediment transport rate was formulated by using the existing sheet flow sediment transport rate data under skew waves by Watanabe and Sato [Watanabe, A. and Sato, S., 2004. A sheet-flow transport rate formula for asymmetric, forward-leaning waves and currents. Proc. of 29th ICCE, ASCE, pp. 1703–1714.]. Moreover, the characteristics of the net sediment transport were also examined and a good agreement between the proposed method and experimental data has been found.     

Turbulence-induced steady streaming in an oscillating boundary layer: On the reliability of turbulence closure models

The accuracy of several closure models of the Reynolds-Averaged Navier–Stokes Equations in predicting the characteristics of an oscillating turbulent wall boundary layer is analyzed. The analysis involves four low Reynolds number k − ε models and a k − ω model and it is carried out by comparing the model results both with experimental data and with data obtained by a Direct Numerical Simulation (DNS) of the Navier–Stokes equations. The boundary layer is generated by a spatially constant time-oscillating pressure gradient given by the sum of two harmonic components characterized by angular frequencies Ω^∗ and 2Ω^∗ respectively, which generates a steady streaming because of the asymmetry of turbulence intensity during the cycle. Thus the results are relevant to the boundary layer at the bottom of nonlinear sea waves. The attention is therefore focused on the accuracy of the models in reproducing the period averaged profiles of the hydrodynamic characteristics of the steady streaming. The instantaneous quantities, such as time development of the wall shear stress, profiles of the streamwise velocity, Reynolds stresses and turbulent kinetic energy are also considered and analyzed. The results shows that a model can be judged better or worse than other models depending on the specific flow characteristic under investigation. However, an approach has been adopted which allowed to rank the models according to their accuracy in predicting the values of the hydrodynamic quantities involved in the present study.