scholarly journals BED SHEAR STRESS IN UNSTEADY FLOW

2011 ◽  
Vol 1 (32) ◽  
pp. 8 ◽  
Author(s):  
Paul Andrew Guard ◽  
Peter Nielsen ◽  
Tom E Baldock
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Water Surface ◽  
Free Stream ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Horizontal Pressure Gradient ◽  
Friction Factors ◽  
Horizontal Pressure

Standard engineering methods of estimating bed shear stress using friction factors can fail spectacularly in unsteady hydrodynamic conditions. This paper demonstrates this fact using direct measurements of bed shear stresses under irregular waves using a shear plate apparatus. The measurements are explained in terms of the influence of the horizontal pressure gradient and the shear stresses acting on the surface of the plate. The horizontal fluid velocity at the edge of the boundary layer and the water surface elevation and slope were also measured. The paper demonstrates that the water surface measurements can be used to obtain accurate estimates of the forces on the bed, by employing Fourier analysis techniques or an innovative convolution integral method. The experimental results indicate that an offshore bed shear stress may be recorded while the free stream velocity remains onshore at all times. This demonstrates the failure of the standard engineering friction factor method in this scenario, since negative friction factors would be required. Important questions are raised regarding the appropriate definition for the bed shear stress when the vertical gradient of the shear stress is large. It is shown that it is problematic to define a single value for a “bed” shear stress in the presence of a strong horizontal pressure gradient. It is also argued that the natural driver for any model used to predict bed shear stress is the pressure gradient (or its proxy the free stream acceleration), rather than the velocity. This allows for accurate calculation of both acceleration effects (more rapid acceleration leads to a thinner boundary layer and higher shear stress) and also the direct action of the horizontal pressure gradient.

Velocity distribution and shear velocity behaviour of decelerating flows over a gravel bed

1999 ◽  
Vol 26 (4) ◽  
pp. 468-475 ◽  
Author(s):  
Hossein Afzalimehr ◽  
François Anctil
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Outer Region ◽  
Shear Velocity ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Gravel Bed ◽  
Parabolic Law

The behaviour of the bed shear stress in the presence of a decelerating flow over a gravel bed has been examined. The collected observations revealed that the velocity distribution in the outer region of the boundary layer may be described by a parabolic law. The results obtained by parabolic law are comparable to the bed shear stress estimated via the St-Venant method. At a specific cross section, shear velocities estimated by the parabolic and the St-Venant methods divert considerably from the estimation by zero pressure gradient method. For constant bottom slope and relative roughness, the estimated bed shear stresses based on the parabolic and the St-Venant methods are proportional to the flow discharge, whereas this tendency is not accounted for by the zero pressure gradient model.Key words: velocity distribution, shear velocity, decelerating flows, gravel bed, boundary layer.

The Relationships among Wind, Horizontal Pressure Gradient, and Turbulent Momentum Transport during CASES-99

2013 ◽  
Vol 70 (11) ◽  
pp. 3397-3414 ◽  
Author(s):  
Jielun Sun ◽  
Donald H. Lenschow ◽  
Larry Mahrt ◽  
Carmen Nappo
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Pressure Gradient ◽  
Coriolis Force ◽  
Wind Direction ◽  
Momentum Flux ◽  
Momentum Transport ◽  
Horizontal Pressure Gradient ◽  
Horizontal Pressure ◽  
Turbulent Momentum

Abstract Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground occurred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s−1, WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP. In the along-wind direction, the horizontal pressure gradient is observed to be well correlated with the quadratic wind speed, which is demonstrated to be an approximate balance between the horizontal pressure gradient and the vertical convergence of the turbulent momentum flux. That is, antitriptic balance occurs in the along-wind direction when the wind is toward higher pressure. In the crosswind direction, the pressure gradient varies approximately linearly with wind speed and opposes the Coriolis force, suggesting the importance of the Coriolis force and approximate geotriptic balance of the airflow. A simple one-dimensional planetary boundary layer eddy diffusivity model demonstrates the possibility of wind directed toward higher pressure for a baroclinic boundary layer and the contribution of the vertical turbulent momentum flux to this phenomenon.

scholarly journals MEASUREMENT AND MODELING OF SOLITARY WAVE INDUCED BED SHEAR STRESS OVER A ROUGH BED

2012 ◽  
Vol 1 (33) ◽  
pp. 21 ◽  
Author(s):  
Jaya Kumar Seelam ◽  
Tom E Baldock
Keyword(s):  
Shear Stress ◽  
Eddy Viscosity ◽  
Breaking Waves ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Eddy Viscosity Model ◽  
Friction Factors ◽  
Convolution Model ◽  
Rough Bed ◽  
Bed Shear Stresses

Bed shear stresses generated by solitary waves were measured using a shear cell apparatus over a rough bed in laminar and transitional flow regimes (~7600 < Re < ~60200). Modeling of bed shear stress was carried out using analytical models employing convolution integration methods forced with the free stream velocity and three eddy viscosity models. The measured wave height to water depth (h/d) ratio varied between 0.13 and 0.65; maximum near- bed velocity varied between 0.16 and 0.47 m/s and the maximum total shear stress (sum of form drag and bed shear) varied between 0.565 and 3.29 Pa. Wave friction factors estimated from the bed shear stresses at the maximum bed shear stress using both maximum and instantaneous velocities showed that there is an increase in friction factors estimated using instantaneous velocities, for non-breaking waves. Maximum positive total stress was approximately 2.2 times larger than maximum negative total stress for non-breaking waves. Modeled and measured positive total stresses are well correlated using the convolution model with an eddy viscosity model analogous to steady flow conditions (nu_t=0.45u* z1; where nu_t is eddy viscosity, u* is shear velocity and z1 is the elevation parameter related to relative roughness). The bed shear stress leads the free stream fluid velocity by approximately 30° for non-breaking waves and by 48° for breaking waves, which is under-predicted by 27% by the convolution model with above mentioned eddy viscosity model.

Reynolds-shear-stress measurements in a compressible boundary layer within a shock-wave-induced adverse pressure gradient

1974 ◽  
Vol 65 (1) ◽  
pp. 177-188 ◽  
Author(s):  
W. C. Rose ◽  
M. E. Childs
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Heat Transfer ◽  
Shear Stresses ◽  
Turbulent Heat ◽  
Wave Induced

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer-thickness Reynolds number were 4 and 105, respectively. The adverse pressure gradient was induced by an externally generated, conical shock wave.Mean and time-averaged fluctuating-flow data, including the experimental Reynolds shear stresses and experimental turbulent heat-transfer rates, are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed.From the results of the investigation, it is concluded that the shock-wave/boundary-layer interaction significantly alters the shear-stress characteristics of the boundary layer.

scholarly journals Direct Measurements of Bed Shear Stress under Swash Flows on Steep Laboratory Slopes at Medium to Prototype Scales

2019 ◽  
Vol 7 (10) ◽  
pp. 358 ◽  
Author(s):  
Howe ◽  
Blenkinsopp ◽  
Turner ◽  
Baldock ◽  
Puleo
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Steady Flows ◽  
Swash Zone ◽  
Wave Runup ◽  
Transport Modelling ◽  
Friction Factors ◽  
Direct Measurements

Robust measurements of bed shear stress under wave runup flows are necessary to inform beachface sediment transport modelling. In this study, direct measurements of swash zone bed shear stress were obtained in medium and prototype-scale laboratory experiments on steep slopes. Peak shear stresses coincided with the arrival of uprush swash fronts and high-resolution measurement of swash surface profiles indicated a consistently seaward sloping swash surface with minimal evidence of a landward sloping swash front. The quadratic stress law was applied to back-calculate time-varying friction factors, which were observed to decrease with increasing Reynolds number on smooth slopes, consistent with theory for steady flows. Additionally, friction factors remained relatively constant throughout the swash cycle (except around flow reversal), with a variation of approximately ±20% from the mean value and with only small differences between uprush and backwash. Measured friction factors were observed to be larger than expected when plotted on the Moody or wave friction diagram for a given Reynolds number and relative roughness, consistent with previous field and laboratory studies at various scales.

scholarly journals Mean flow structure and velocity–bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: direct numerical simulations

2021 ◽  
Vol 928 ◽  
Author(s):  
Dimitrios K. Fytanidis ◽  
Marcelo H. García ◽  
Paul F. Fischer
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Numerical Simulations ◽  
Phase Difference ◽  
Free Stream ◽  
Direct Numerical Simulations ◽  
Stream Velocity ◽  
Phase Lag ◽  
Bed Shear Stress ◽  
Oscillatory Boundary Layer

Direct numerical simulations of oscillatory boundary-layer flows in the transitional regime were performed to explain discrepancies in the literature regarding the phase difference ${\rm \Delta} \phi$ between the bed-shear stress and free-stream velocity maxima. Recent experimental observations in smooth bed oscillatory boundary-layer (OBL) flows, showed a significant change in the widely used ${\rm \Delta} \phi$ diagram (Mier et al., J. Fluid Mech., vol. 922, 2021, A29). However, the limitations of the point-wise measurement technique did not allow us to associate this finding with the turbulent kinetic energy budget and to detect the approach to a ‘near-equilibrium’ condition, defined in a narrow sense herein. Direct numerical simulation results suggest that a phase lag occurs as the result of a delayed and incomplete transition of OBL flows to a stage that mimics the fully turbulent regime. Data from the literature were also used to support the presence of the phase lag and propose a new ${\rm \Delta} \phi$ diagram. Simulations performed for ${\textit {Re}}_{\delta }=671$ confirmed the sensitivity in the development of self-sustained turbulence on the background disturbances ( $\textit{Re}_{\delta}=U_{o}\delta/\nu$ , where $\delta=[2\nu/\omega]^{1/2}$ is the Stokes' length, $U_{o}$ is the maximum free stream velocity of the oscillation, $\nu$ is the kinematic viscosity and $\omega=2{\rm \pi}/T$ is the angular velocity based on the period of the oscillation T). Variations of the mean velocity slope and intersect values for oscillatory flows are also explained in terms of the proximity to near-equilibrium conditions. Relaminarization and transition effects can significantly delay the development of OBL flows, resulting in an incomplete transition. The shape and defect factors are examined as diagnostic parameters for conditions that allow the formation of a logarithmic profile with the universal von Kármán constant and intersect. These findings are of relevance for environmental fluid mechanics and coastal morphodynamics/engineering applications.

scholarly journals IMPROVEMENT OF BOTTOM BOUNDARY LAYERS MODELING UNDER INTERACTIONS OF WAVE AND WAVE-INDUCED CURRENT

2011 ◽  
Vol 1 (32) ◽  
pp. 46
Author(s):  
Jinhai Zheng ◽  
Chi Zhang ◽  
Yigang Wang ◽  
Zeki Demirbilek
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Bottom Boundary Layer ◽  
Induced Current ◽  
Horizontal Pressure Gradient ◽  
Bottom Boundary ◽  
Bottom Boundary Layers ◽  
Horizontal Pressure ◽  
The Mean ◽  
Wave Induced

The bottom boundary layer characteristics beneath waves transforming on a natural beach are specifically affected both by wave and wave-induced current. This study presents an improved approach for coastal bottom boundary layers modeling under interactions of wave and wave-induced current. The improvement is achieved by formulating the mean horizontal pressure gradient term in the boundary layer equation with wave parameters and mean water level. This formulation represents the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient in a spatially transforming wave field, accounting for the effect of the wave-induced cross-shore current. Model is validated with experimental data for normally incident shoaling wave over a sloping bed. Calculated results agree well with data for instantaneous velocity profiles, wave oscillating amplitudes and mean velocity profiles. In particular, model reasonably reproduces the observed local onshore mean flow near the bottom beneath shoaling wave. It is revealed that the proposed formulation of the mean horizontal pressure gradient plays an important role in bottom boundary layer modeling under wave transforming over an variable near-shore bathymetry, and that the present model can be conveniently and reliably coupled with a sediment transport model to study coastal processes in engineering applications.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

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