Oscillatory Boundary Layer Flow Research Articles

PIV experiments in rough-wall, laminar-to-turbulent, oscillatory boundary-layer flows

Exploratory measurements of oscillatory boundary layers were conducted over a smooth and two different rough beds spanning the laminar, transitional and turbulent flow regimes using a multi-camera 2D-PIV system in a small oscillatory-flow tunnel (Admiraal et al. in J Hydraul Res 44(4):437–450, 2006). Results show how the phase lag between bed shear stress and free-stream velocity is better defined when the integral of the momentum equation is used to estimate the bed shear stress. Observed differences in bed shear stress and phase lag between bed shear stress and free-stream velocity are highly sensitive to the definition of the bed position (y = b). The underestimation of turbulent stresses close to the wall is found to explain such differences when using the addition of Reynolds and viscous stresses to define both the bed shear stress and the phase lag. Regardless of the flow regime, in all experiments, boundary-layer thickness reached its maximum value at a phase near the flow reversal at the wall. Friction factors in smooth walls are better estimated using a theoretical equation first proposed by Batchelor (An introduction to fluid dynamics. Cambridge University Press, Cambridge, 1967) while the more recent empirical predictor of Pedocchi and Garcia (J Hydraul Res 47(4):438–444, 2009a) was found to be appropriate for estimating friction coefficients in the laminar-to-turbulent transition regime.

BIOLUMINESCENCE IMAGING FOR MEASURING FLUID SHEAR DISTRUBUTIONS

The dinoflagellate Pyrocystis lunula emits light in response to water motion. The statistical features of the bioluminescence, emitted by P. lunula, owing to shear stress in oscillatory boundary layer flows over ripped bed were studied in this paper with the aim to develop a new imaging technique for measuring fluid strain rate and shear using plankton that emit light in response to mechanical stimulation. The flash intensity has been found to correlate with fluid strain rate estimated from fluid velocity over ripples. Thus the instantaneous planar distribution of the fluid shear can be estimated from video images of the bioluminescence in a fluid region by using the empirical relation determined in this study.

THE EFFECT OF BED PERMEABILITY ON OSCILLATORY BOUNDARY LAYER FLOW

This experimental study consists of a series of full-scale experiments involving oscillatory boundary layer flow over an impermeable bed and a permeable bed. Velocity measurements have been obtained through particle image velocimetry, and the effect of bed permeability on the velocity profile, phase lead, boundary layer thickness, bed shear stress (as estimated by fitting the log law), and finally the resulting friction factor is presented. For our rough turbulent flows over a permeable bed it has been found that the friction factor is increased by up to 36% and that the friction factor also demonstrates a dependence on Reynolds number.

On the vertical and temporal structure of flow and stress within the turbulent oscillatory boundary layer above evolving sand ripples

Abstract The vertical structure of flow and stress within turbulent oscillatory boundary layers above evolving sand ripples is investigated in experiments carried out using a prototype wide-band coherent Doppler profiler in an oscillating boundary facility with beds of 0.216 mm median diameter sand, 10 s oscillation period, and 0.9 m excursion (Shields parameter=0.11). The bed evolved from an initial nominally flat state through 5 cm wavelength, nearly two-dimensional ripples to 12 cm wavelength, three-dimensional ripples. Average ripple height increased from 0.2 cm to 1.4 cm, corresponding to roughness Reynolds numbers between 68 and 7700. Average ripple steepness increased from 0.03 to 0.15. Bed elevation spectra exhibit the shift towards lower spatial frequencies observed by Davis et al. (2004) and, at higher spatial frequencies, a saturation range analogous to that in surface gravity wave spectra. Horizontal velocity profiles exhibit the phase lead and overshoot expected for oscillatory boundary layer flow. Bottom stress estimates are obtained from the acceleration defect, the Reynolds stress and the law-of-the-wall. The defect stress estimates are bounded above and below by the Reynolds stress and the law-of-the-wall estimates, respectively. The values of the bottom friction coefficient and hydraulic roughness from the defect stress estimates are consistent with results from previous work on equilibrium orbital-scale ripples, as summarized by Nielsen (1992) , indicating that ripple evolution was quasi-steady.

Roughness-induced streaming in turbulent wave boundary layers

[1] A comprehensive numerical study of oscillatory wave boundary layers on spatially varying bottom roughness is presented. The study utilizes a model solving incompressible Reynolds-averaged Navier-Stokes equations coupled with k-ω turbulence closure, modified in a simple way to incorporate anisotropy in turbulent normal stresses. The model is first validated via comparison with existing oscillating tunnel measurements involving sudden bottom roughness transitions. It is then used to parametrically study oscillatory boundary layer flows, wherein the bed shear stress amplifications and period-averaged streaming characteristics induced by bottom roughness variations are systematically assessed. The effects of variable roughness ratio, gradual roughness transitions, as well as changing flow orientation in plan are all considered. As part of the latter, roughness-induced secondary flows are predicted to occur as the oscillatory flow becomes oriented parallel to a line of roughness transition. This phenomenon is proposed as a natural transverse grain sorting mechanism for coastal flows over graded sediments. Subsequent model testing demonstrates potential generation of secondary circulation cells having characteristic size the order of the wave boundary layer thickness. Analogy is made to similar features known to develop within steady flows, having characteristic size the order of the flow depth.

Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow

AbstractExperiments have been conducted in a large oscillatory flow tunnel to investigate the effects of acceleration skewness on oscillatory boundary layer flow over fixed beds. As well as enabling experimental investigation of the effects of acceleration skewness, the new experiments add substantially to the relatively few existing detailed experimental datasets for oscillatory boundary layer flow conditions that correspond to full-scale sea wave conditions. Two types of bed roughness and a range of high-Reynolds-number, $\mathit{Re}\ensuremath{\sim} O(1{0}^{6} )$, oscillatory flow conditions, varying from sinusoidal to highly acceleration-skewed, are considered. Results show the structure of the intra-wave velocity profile, the time-averaged residual flow and boundary layer thickness for varying degrees of acceleration skewness, $\ensuremath{\beta} $. Turbulence intensity measurements from particle image velocimetry (PIV) and laser Doppler anemometry (LDA) show very good agreement. Turbulence intensity and Reynolds stress increase as the flow accelerates after flow reversal, are maximum at around maximum free-stream velocity and decay as the flow decelerates. The intra-wave turbulence depends strongly on $\ensuremath{\beta} $ but period-averaged turbulent quantities are largely independent of $\ensuremath{\beta} $. There is generally good agreement between bed shear stress estimates obtained using the log-law and using the momentum integral equation, and flow acceleration skewness leads to high bed shear stress asymmetry between flow half-cycles. Turbulent Reynolds stress is much less than the shear stress obtained from the momentum integral; analysis of the stress contributors shows that significant phase-averaged vertical velocities exist near the bed throughout the flow cycle, which lead to an additional shear stress, $\ensuremath{-} \rho \tilde {u} \tilde {w} $; near the bed this stress is at least as large as the turbulent Reynolds stress.

Acoustic measurement of suspended sediment concentration profiles in an oscillatory boundary layer

Abstract The use of an Ultrasonic Velocity Profiler (UVP) to obtain phase-averaged velocity and turbulent Reynolds stress profiles inside an oscillatory boundary layer flow is described in detail and possible error sources are summarized. Since the instrument also reports the acoustic backscatter, a novel application of the same ultrasound profilers to obtain phase-averaged suspended sediment concentration profiles and the errors involved in this technique are carefully discussed. The experiments were performed in the Large Oscillatory Water-Sediment Tunnel (LOWST), which has been a recent addition to the experimental facilities of the Ven Te Chow Hydrosystems Laboratory at the University of Illinois at Urbana-Champaign. The results showed that for the selected transducer frequency and flow, the instrument ability to characterize turbulence is compromised by the presence of Doppler noise and the size of the sampling volume. Regarding the suspended sediment estimation, it was found that the calibration obtained using water samples yielded good results, allowing for the study of the suspended sediment evolution along the oscillation.

LATTICE BOLTZMANN SIMULATION TO CHARACTERIZE ROUGHNESS EFFECTS OF OSCILLATORY BOUNDARY LAYER FLOW OVER A ROUGH BED

The 3-D lattice Boltzmann method was applied to characterize roughness effects of oscillatory boundary layer flow over a rough bed. The direct numerical simulation was carried out and the flow resistance of the flat and fixed bed was investigated. The position of the theoretical bed, equivalent roughness height and the behavior of friction factor at small values of relative roughness were obtained using the log-fit method.

Turbulent kinetic energy balance of an oscillatory boundary layer in the transition to the fully turbulent regime

The sinusoidal oscillation of a fluid in the vicinity of a rigid smooth wall is studied using the results of direct numerical simulation of the Navier–Stokes equations. Simulations are performed at a wave Reynolds number Rew =U max A/ν=1.41×106 in the turbulent regime. The computed statistics are compared with great success with the available experimental results reported in the literature for U max =1.02 m/s the maximum orbital velocity, A=1.58 m the amplitude of the water excursion, and ν=1.14×10−6 m2/s the kinematic viscosity of the fluid (Rew =U max A/ν=1.41×106). The simulation results allow to identify the development of an unsteady shear layer and regions of zero and negative turbulent kinetic energy (TKE) production. The TKE balance is studied in detail, analyzing the role of each of the terms in the balance equation and the relative relevance of different TKE transport mechanisms. It is found that the local derivative of the TKE is particularly important in the shear layer region. The present results provide an accurate and detailed dataset that could be used for validation of both analytical and numerical models of oscillatory boundary layer flows.

Bioluminescence Imaging Measurements of oscillatory shear flows

In this paper, flashing responses of bioluminescent dinoflagellates in oscillatory turbulent boundary layer flows over rippled bed are studied with the aim with future development of imaging technique to aquire planar distributions of turbulence in a shear layer. Foundamental statistical properties of the bioluminescence involved in strong turbulence caused by separation of the boundary layer from the ripple crest are discussed, and it is found that there is a correlation of time variation of the mean flash intensity with the turbulent energy.

Implementation of physical boundary conditions into computational domain in modelling of oscillatory bottom boundary layers

AbstractThis paper discusses the importance of realistic implementation of the physical boundary conditions into computational domain for the simulation of the oscillatory turbulent boundary layer flow over smooth and rough flat beds. A mathematical model composed of the Reynolds averaged Navier–Stokes equation, turbulent kinetic energy (k) and dissipation rate of the turbulent kinetic energy (ε) has been developed. Control‐volume approach is used to discretize the governing equations to facilitate the numerical solution. Non‐slip condition is imposed on the bottom surface, and irrotational main flow properties are applied to the upper boundary. The turbulent kinetic energy is zero at the bottom, whereas the dissipation rate is approaching to a constant value, which is proportional to the kinematic viscosity times the second derivative of the turbulent kinetic energy. The output of the model is compared with the available experimental studies conducted in oscillatory tunnels and wave flume. It is observed that the irrotational flow assumption at the upper boundary is not realistic in case of water tunnels. Therefore, new upper boundary conditions are proposed for oscillatory tunnels. The data of wave flume show good agreement with the proposed numerical model. Additionally, several factors such as grid aspect ratio, staggered grid arrangement, time‐marching scheme and convergence criteria that are important to obtain a robust, realistic and stable code are discussed. Copyright © 2009 John Wiley & Sons, Ltd.

Friction coefficient for oscillatory flow: the rough–smooth turbulent transition

Observations of turbulent, oscillatory boundary-layer flows show that the behavior of the friction coefficient in the transition from hydraulically rough to smooth regimes is not well captured by existing semi-empirical expressions obtained for unidirectional flows.A revised formulation for the friction coefficient for oscillatory flows is presented. Dimensional analysis and similarity methods are used to assess the dimensionless parameters governing the relation between the outer flow and the bottom shear stress. Further progress is made using analogies between oscillatory and unidirectional boundary layer flows, from which analytical expressions are calibrated. An expression for the phase lead between the maximum bed shear stress and the maximum free-stream velocity is obtained. An example describing the computational procedure needed to estimate the friction coefficient and phase lead using the new expressions is presented to show their practical application to both laboratory and field conditions.

Flow tunnel measurements of velocities and sand flux in oscillatory sheet flow for well-sorted and graded sands

Oscillatory flow tunnel measurements of velocities and fluxes for sands in oscillatory sheet flow conditions are presented. The experiments involved a range of well-sorted and graded sands in two asymmetric flows. Velocities were measured using an ultrasonic velocity profiler (UVP) capable of measuring deep within the sheet flow layer. Velocity profiles are found to be similar for the same flow but different sand beds and display expected features of oscillatory boundary layer flow. The near-bed velocity leads the main flow velocity by approximately 21° and a small offshore-directed current is generated near the bed. Measures of the boundary layer thickness are in good agreement with those predicted using an equation formulated for the boundary layer thickness over fixed beds. Velocity data have been combined with concentration data to produce time-dependent sand flux profiles covering the sheet flow and suspension regions. There are fundamental differences in the transport processes of sands of different size and grading, caused by unsteady effects which dominate in the case of fine sand and are largely absent in the case of coarse sand. (1) Time-averaged flux is onshore-directed (positive) in the case of coarse sand and is confined to a region immediately above the bed; in contrast, time-averaged flux in the case of fine sand extends high above the bed, is offshore-directed (negative) in the sheet flow layer and becomes onshore-directed in the suspension layer. (2) Net transport in the case of coarse sand is directed onshore. As the percentage of fine sand in the bed increases, offshore transport becomes increasingly dominant as the percentage of fine sand increases. (3) Net transport in the suspension layer is onshore while net transport in the sheet-flow layer may be onshore or offshore depending on sand size and grading.

Temperature distribution in an oscillatory flow with a sinusoidal wall temperature

Abstract The temperature field generated by an oscillatory boundary layer flow in the presence of a wall with a sinusoidal temperature distribution is analyzed. A linear perturbation method is used to find closed form analytical solutions for the temperature field when the amplitude of the velocity oscillation is small. The analytical solutions only consider long-time behavior when the temperature fields oscillate with the frequency of the flow. The structure of the equation that governs the temperature correction due to convection is similar to that of diffusive waves with the solution consisting of traveling or standing waves. The temperature distribution is also solved numerically which allows a description of the transient and periodic temperature fields. At short times, the solution has similarities with the traveling waves, while at long times the solution evolves toward a standing wave. As the amplitude of the solution is increased, beyond the linear approximation, the temperature oscillation remains periodic, but more Fourier modes are incorporated. We find that in all cases, the long-time, time averaged heat transfer from the boundary to the fluid is zero.

An oscillating hydromagnetic non-Newtonian flow in a rotating system

An exact solution of an oscillatory boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and the other at rest, is developed. The fluid and the plates are in a state of solid body rotation with constant angular velocity about the z -axis normal to the plates. The fluid is assumed to be second grade, incompressible, and electrically conducting. A uniform transverse magnetic field is applied. During the mathematical analysis, it is found that the steady part of the solution is identical to that of viscous fluid. The structure of the boundary layers is also discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.

A depth-of-field limited particle image velocimetry technique applied to oscillatory boundary layer flow over a porous bed

Boundary layer flows are ubiquitous in the environment, but their study is often complicated by their thinness, geometric irregularity and boundary porosity. In this paper, we present an approach to making laboratory-based particle image velocimetry (PIV) measurements in these complex flow environments. Clear polycarbonate spheres were used to model a porous and rough bed. The strong curvature of the spheres results in a diffuse volume illuminated region instead of the more traditional finite and thin light sheet illuminated region, resulting in the imaging of both in-focus and significantly out-of-focus particles. Results of a traditional cross-correlation-based PIV-type analysis of these images demonstrate that the mean and turbulent features of an oscillatory boundary layer driven by a free-surface wave over an irregular-shaped porous bed can be robustly measured. Measurements of the mean flow, turbulent intensities, viscous and turbulent stresses are presented and discussed. Velocity spectra have been calculated showing an inertial subrange confirming that the PIV analysis is sufficiently robust to extract turbulence. The presented technique is particularly well suited for the study of highly dynamic free-surface flows that prevent the delivery of the light sheet from above the bed, such as swash flows.

An Oscillatory Hydromagnetic Couette Flow in a Rotating System

An exact solution of hydromagnetic oscillatory Ekman boundary layer flow of an electrically conducting fluid between two parallel flat plates, one of which is at rest and the other oscillating in its own plane, is obtained when the entire system rotates about an axis normal to the plates. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. For M = 0, the problem reduces to the one discussed by Ganapathy [8]. During the mathematical analysis it is found that even the claim of Ganapathy [8] that the solution of Mazumder [7] explains the important phenomenon of resonance in rotating systems is incorrect.

10.1016/s0967-0653(95)97518-7

10.1016/s0967-0653(95)97518-7

Steady streaming in oscillatory viscous flow under a transverse magnetic field

In this paper we deal with the oscillatory laminar boundary layer flow of an electrically conducting fluid near an insulating solid body under a transverse, uniform magnetic field. It is assumed that the two-dimensional flow is produced by an external stream velocity which varies periodically and that the magnetic field induced in the fluid can be neglected. The solution of the boundary layer equations is found by an expansion on the small parameter ε (the inverse of the Strouhal number). Both the primary oscillatory flow and the secondary flow which is composed of an oscillatory motion and a steady contribution, i.e. the steady streaming, are analytically determined. The magnetohydrodynamic (MHD) flow correctly reduces to the hydrodynamic limit when the magnetic field vanishes. However, differently from the hydrodynamic case, the MHD second order steady solution satisfies the vanishing of the steady streaming motion as the distance from the body tends to infinity. This result is a consequence of the suppression of the only vorticity component, which is perpendicular to the magnetic field. Further, when the magnetic interaction parameter is sufficiently high, the streaming motion can be completely suppressed.

Oscillatory boundary layer flows modelled with dynamic Reynolds stress turbulence closure

Abstract A standard dynamic Reynolds stress model, with conventional coefficients, is applied to oscillatory boundary layer flows. With a grid resolution over the boundary layer thickness and wave period of the order of 100 and 600 respectively, well defined, grid-independent solutions are obtained. The available data are predicted in great detail. However, even with turbulence characteristics, the data from oscillatory flows do not appear to be very model discriminant. A model based upon a standard ( k -ɛ) closure also predicts them reasonably realistically. With sediment entrainment, giving stably stratified flow, the Reynolds stress model estimates that there is almost no turbulence above the mean velocity maximum. This is probably a reason why a ( k -ɛ) model even predicts such flows accurately. Another reason is that the flow is strongly forced (by the oscillatory pressure gradient) and is not, like for instance turbidity currents, decisively governed by the turbulence. An oscillatory flow with sediment entrainment on a slope is predicted to force a systematic turbidity current. At large enough slope angles, the waves are predicted to trigger self-accelerated turbidity currents.