Logarithmic Boundary Layer Research Articles

A logarithmic bottom boundary layer model for the unsteady and non-uniform swash flow

This paper presents a bottom boundary layer model for the unsteady and non-uniform flow in the swash zone, by extending the momentum integral method so as to include spatial gradients. The developed model is further incorporated into a hydrodynamic model based on the Nonlinear Shallow Water Equations. Two swash zone cases are examined to investigate the effect of the inclusion of spatial gradients. In the first of the two, boundary layer development under non-breaking periodic waves formulated by Carrier and Greenspan (1958) is investigated (wave-driven swash). Results show that the spatial gradients have the most pronounced effect in the lower swash, and in the region just seaward. In both these regions the spatial gradients enhance (diminish) onshore (offshore) bed shear stress, thus potentially contributing to onshore sediment transport under non-breaking waves. The second case investigated is the Kikkert et al. (2012) dam-break swash event (bore-driven swash). The model results are qualitatively and quantitatively accurate when compared against the laboratory measurements, and the velocities in the later backwash agree more closely with the measurements than those of Briganti et al. (2011). Results show that the inclusion of spatial gradients also favours onshore sediment transport in the lower swash. In addition, the bottom boundary layer is more fully developed in the uprush tip, resulting in smaller bed shear stress in the upper swash. The extended momentum integral method thus appears to capture more comprehensively the swash boundary layer, and the approach, therefore, offers a way forward in more accurate reproduction of swash dynamics in computational modelling.

Thermoviscous fluid flow in nonisothermal layer: structures, scales, and correlations

The paper studies turbulent mixing in thermoviscous fluid flow in a 3D cubic domain which is extended periodically in two directions (X and Y). The flow turbulization develops under the impact of two-dimensional chaotic disturbances at mass average Reynolds number Re1 = 4704. The vortex field structure is discussed in terms of an isosurface of Q-criterion and local enstrophy ζ1. For the advanced stages of flow evolution, the study considers Eulerian correlation coefficients for velocity fluctuations (auto-correlation functions) and the cross-correlations of pressure and temperature. The Eulerian correlation coefficient is split for analysis of correlation characteristics in periodicity and wall-normal directions. The integral scale is evaluated depending on the distance to the walls. The flow analysis is performed in the terms of viscous scale. The mesh resolution is evaluated for the flow regions corresponding to the logarithmic boundary layer and the near-wall thermal layers.

Large-eddy simulation of an open-channel flow bounded by a semi-dense rigid filamentous canopy: Scaling and flow structure

We have carried out a large-eddy simulation of a turbulent open-channel flow over a marginally dense, fully submerged, rigid canopy. The canopy is made of a set of rigid, slender cylinders normally mounted on a solid wall. The flow in the canopy is resolved stem-by-stem by means of an immersed boundary method. It is found that the flow behavior can be categorized according to the velocity distribution into two separate spatial regions: the canopy itself and the outer region above it. Within the region occupied by the canopy elements, the velocity magnitude is found to be related to the local shear stress. Outside the canopy, a logarithmic velocity profile matching the canonical turbulent open-channel flow over rough walls is recovered albeit the strong manipulation exerted by the canopy on the buffer layer. In the innermost layer, the presence of the stems is responsible for redistributing the local momentum fluctuations from a streamwise to a spanwise leading component, inhibiting the survival of the wall streamwise velocity streaks. On the other hand, the outer region presents a structure very similar to the well-known logarithmic boundary layer with the presence of large and energetic streamwise velocity streaks generated by a system of quasistreamwise vortices. These vortices strongly contribute to the intracanopy fluctuations through vigorous sweep and ejection events that affect all the region occupied by the stems. Consistent with the results of previous investigations [H. Nepf, “Flow and transport in regions with aquatic vegetation,” Annu. Rev. Fluid Mech. 44, 123–142 (2012)], it is found that the inflection point in the mean velocity profile, produced by the drag discontinuity at the canopy tip, promotes the appearance of another system of spanwise oriented vorticity structures. However, different from previous results reported in the literature [J. Finnigan, “Turbulence in plant canopies,” Annu. Rev. Fluid Mech. 32, 519–571 (2000)], in our simulations, the presence of alternating head up–head down hairpin vortices generated by a mutual induction of the counter-rotating spanwise vortices is not observed. Instead, we advocate that the modulation of the spanwise coherent vorticity is due to the action of the external logarithmic layer structures (i.e., the outer streamwise vortices that penetrate the canopy) rather than by upwash and downwash motions induced by the mutual interaction of the spanwise rollers.

Surface-groundwater flow numerical model for barrier beach with exfiltration incorporated bottom boundary layer model

A surface-groundwater flow model is developed for the swash flow on a barrier beach. The non-linear shallow water equations are used to simulate the surface flow. Laplace's equation is used to describe the groundwater flow and is solved using the Boundary Integral Equation Method to provide potential heads and normal potential derivatives at and within the boundaries of the barrier. An exfiltration incorporated bottom boundary layer sub-model is used to obtain bed shear stress. The groundwater model is verified against the numerical test results in Kazemzadeh-Parsi and Daneshmand (2012) for the groundwater flow through a rectangular dam. The coupled surface-groundwater model is validated against the prototype-scale BARDEX II experimental results (Turner et al., 2016). The steady-state groundwater flow comparisons show excellent agreement in phreatic surfaces. The comparisons of groundwater flow under the action of waves show reasonably good agreement with experimental results in phreatic surfaces. The simulated time averaged pore velocities for the runs with and without waves are in satisfactory agreement with experimental results in general, and certain discrepancies are observed near the beach side. The bed shear stress variation due to exfiltration is investigated by incorporating the modified logarithmic bottom boundary layer model of Cheng and Chiew (1998) in the coupled surface-groundwater flow model. The results confirm that as exfiltration increases, bed shear stress decreases as a result of thickening of the bottom boundary layer.

Large Eddy simulations of flow around tandem circular cylinders in the vicinity of a plane wall

To investigate the three-dimensional flow around free-spanning, tandem marine pipelines, Large Eddy Simulations (LES) with Smagorinsky subgrid scale model are performed using the open-source code OpenFOAM. Two circular cylinders in tandem arrangement are placed in the vicinity of a rigid, horizontal, plane wall. The cylinders are immersed in a steady current with a logarithmic boundary layer profile at an intermediate, subcritical Reynolds number (Re = 1.31 × 104). The non-dimensional distances between the cylinder centres are 2 and 5 (L/D = 2 and 5) and the gap to diameter ratios are G/D = 0.6 and 1, where gap G is the distance between the bottom of the cylinders and the wall. The present results are analysed through the values of drag and lift coefficients, as well as by the details of the flow fields in the wake of the cylinders. The results are compared with experimental results of the flow around tandem cylinders in an unlimited fluid for both L/D = 2 and 5, showing that, at chosen gaps, at L/D = 2, the flow belongs to the reattachment regime, and at L/D = 5 to the co-shedding regime. Compared with the case of a single cylinder near a plane wall, the flow around the tandem cylinders at G/D = 1 belongs to the wide gap regime, while at G/D = 0.6, tandem yields a stronger interaction with the wall than in the case of one cylinder. The presence of the wall modifies the flow in the spacing between the two cylinders, giving it some characteristics of the extended body flow regime.

On the compatibility of a logarithmic turbulent boundary layer velocity profile with experimental data

On the compatibility of a logarithmic turbulent boundary layer velocity profile with experimental data

Large Eddy Simulations of flow around a circular cylinder close to a flat seabed

Large Eddy Simulations (LES) with Smagorinsky subgrid scale model are used to study the turbulent flow and wake dynamics behind a circular cylinder close to a horizontal, plane wall at subcritical Reynolds number. The focus is on investigating the details of the flow around the cylinder placed at different distances from the wall and immersed in boundary layers of various thicknesses.The Reynolds number is Re = 13,100. The simulations with gap to diameter ratios (G/D) of 0.2, 0.6 and 1 are carried out in order to investigate the changes of the flow field and the vortex shedding due to the presence of the plane wall. The influence of the incoming boundary layer profile is investigated through simulations with logarithmic boundary layer inlet profile of thickness 0.48D and 1.6D, and compared with a uniform inlet flow profile. 2D and 3D simulations are performed for Re ranging from 100 to 13,100, to explore the importance of the flow three-dimensionality. The flow field in the cylinder wake, as well as the mean flow values, the spectral analysis and the pressure distribution on the cylinder surface are computed to study the flow physics due to the influences of the wall.

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

SummaryWe perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.

Boundary layer flow dynamics at a cold-water coral reef

The Tisler cold-water coral reef is a 2km long reef in the north-eastern Skagerrak, Norway. The reef is comprised principally of Lophelia pertusa at depths between 70 and 160m. Velocity shear and boundary layer shear stresses have been measured at Tisler Reef to quantify the effect of the reef structure on the benthic boundary layer (BBL) dynamics.Two different approaches to estimating the magnitude of the near seabed stress were employed: using a logarithmic (constant stress) boundary layer approach and direct Reynolds stress measurements. Resultant estimates of near seabed stresses using both methods were comparable.Using the logarithmic layer approach to estimate seabed stresses both inside and out of the reef structure demonstrated that, for any particular impinging flow strength, higher shear stresses were observed within the live coral region than in the dead coral rubble region with no live coral stands. Bottom shear stresses of up to 3.5Nm−2 were measured within the reef complex and 1.2Nm−2 in the rubble region outside the live reef. This difference is due to large roughness length scales inside the rough living coral area relative to the smaller scales in the coral rubble.Low frequency acoustic backscatter data, used as a proxy for relative suspended particulate matter concentrations, suggested that both local re-suspension and advection of suspended material most likely occur at, and through, the reef system. The high stresses measured inside the living reef may favour corals by increasing the degree of re-suspension for a given current speed and providing more particulates to the filter feeding polyps.

Currents, drag, and sediment transport induced by a tsunami

We report observations of water surface elevation, currents, and suspended sediment concentration (SSC) from a 10‐m deep site on the inner shelf in northern Monterey Bay during the arrival of the 2010 Chile tsunami. Velocity profiles were measured from 3.5 m above the bed (mab) to the surface at 2 min intervals, and from 0.1 to 0.7 mab at 1 Hz. SSC was determined from the acoustic backscatter of the near‐bed profiler. The initial tsunami waves were directed cross shore and had a period of approximately 16 min. Maximum wave height was 1.1 m, and maximum current speed was 0.36 m/s. During the strongest onrush, near‐bed velocities were clearly influenced by friction and a logarithmic boundary layer developed, extending more than 0.3 mab. We estimated friction velocity and bed shear stress from the logarithmic profiles. The logarithmic structure indicates that the flow can be characterized as quasi‐steady at these times. At other phases of the tsunami waves, the magnitude of the acceleration term was significant in the near‐bed momentum equation, indicating unsteady flow. The maximum tsunami‐induced bed shear stress (0.4 N/m2) exceeded the critical shear stress for the medium‐grained sand on the seafloor. Cross‐shore sediment flux was enhanced by the tsunami. Oscillations of water surface elevation and currents continued for several days. The oscillations were dominated by resonant frequencies, the most energetic of which was the fundamental longitudinal frequency of Monterey Bay. The maximum current speed (hourly‐timescale) in 18 months of observations occurred four hours after the tsunami arrived.

Observations of Nepheloid Layers in the Yangtze Estuary, China, Through Phase-Corrupted Acoustic Doppler Current Profiler Speeds

AbstractA bottom quadrapod was deployed from March 29 to April 5, 2009 to measure bottom boundary layer (BBL) flows and nepheloid layer properties in the Deepwater Navigation Channel in the North Passage of Shanghai Port in the Yangtze estuary. Using a downward-looking acoustic Doppler current profiler (ADCP) and acoustic Doppler velocimeter, detailed measurements of mean velocity and turbulence distribution within 1 m above the seabed were obtained. It appears that corrupted speeds measured for the deeper bins are caused by formation of the nepheloid layer at the seabed, implying that the ADCP is not a suitable instrument to measure current velocities in the bins nearest the seafloor. A statistical clustering method was used to characterize the current profiles in the BBL. The majority of current profiles within the BBL had a simple shape with current speed monotonically decreasing with depth, reflecting a logarithmic boundary layer. Phase-corrupted ADCP speeds measured for bins close to the bottom are shown to be useful as proxies to indicate the presence of primary and secondary lutoclines/nepheloid layers. A lutocline is a sediment-induced density gradient or pycnocline. The primary lutocline is closest to the bottom, and below it is the nepheloid layer, which is commonly composed of fluid mud. The proxies indicated that a nepheloid layer formed in the neap tide when the current velocity 1 m above the seabed dropped below a threshold of 0.65 m/s. The lutocline height was indicated to be about 0.2 m above the seabed. A secondary lutocline in the water column was also observed in the second half of the record, when the lowest maximum currents occurred.

Modeling the evaporation from a thin liquid surface beneath a turbulent boundary layer

The present study considers the evaporation of a non-buoyant contaminant from a liquid surface beneath a turbulent boundary layer. The analysis is based on near-surface asymptotics of turbulence velocity and scalar fluctuations. The objective of the study is to analytically derive an algebraic evaporation model sensitized to boundary layer turbulence. The dependence on the friction velocity is shown to be naturally included in the analysis and does not depend on any a priori assumption of the existence of an equilibrium logarithmic boundary layer region. The model is validated using recent experimental wind-tunnel data.

A portable wind and rainfall simulator for in situ soil erosion measurements

Abstract Laboratory research in wind tunnels with the capability of simulating rainfall highlighted the importance of considering the complex interactions between wind and rainfall in the analysis of soil erosion processes. In order to overcome the inherent limitations of laboratory research and to further investigate these interactions under comparable conditions in the field, a Portable Wind and Rainfall Simulator (PWRS) has been developed. The aim of this study was to specify the wind and rainfall characteristics of the PWRS and to evaluate if its simulation quality and reproducibility is adequate for comparative soil erosion studies in the field. Wind velocity measurements show that a pre-shaped logarithmic boundary layer with a thickness of about 0.2 m exists. The uniformity of airflow across the tunnel is acceptable within the lower 0.3 m of the tunnel with maximum standard deviations below 0.7 ms − 1 . Maximum variability of wind velocities between three consecutive repetitions of the measurements is lower than 15%. The spatial rainfall distribution for windless rain show rather poor uniformity (Christiansen Uniformity (CU) coefficient = 60%), but very good reproducibility in-between five consecutive replications. About 90% of the test plot experiences a variability of rainfall below 5%. Simulated drop size distributions correspond very well with calculated Marshal–Palmer Distributions (MPD) of equal rainfall intensities (mean deviation of 2.1%). For wind-driven rain both above mentioned parameters clearly improve (CU = 76%, mean deviation = 1.7%). The mean rainfall intensities show also very low variability between the five replications with standard deviations of 0.31 mm h − 1 for windless rain (mean intensity 96 mm h − 1 ) and 0.69 mm h − 1 for wind-driven rain (mean intensity 88 mm h − 1 ). In conclusion, test results of the PWRS are very satisfactory, especially considering the physical constraints, which have to be taken into account to reach desired portability. The analysis presented in this study suggests in particular very good reproducibility of wind and rain conditions. The PWRS should therefore be a useful device for comparative in situ soil erosion measurements in the field and support the gathering of quantitative data on the relative importance of soil detachment rates between wind and water erosion, as well as windless and wind-driven rainfall.

Comparison of a novel profile method to standard chamber methods for measurement of sediment oxygen demand

A methodology is presented to determine the impact of flow rate upon sediment oxygen demand (SOD) based upon dissolved oxygen transport through the logarithmic boundary layer in stream systems. Previous work has used profile methodology to estimate atmospheric fluxes of pollutants from sediment, and similar principles are applied in this study. Chamber and profile SOD measurements were collected on July 21, 2009 in the Millstone River in Hillsborough, NJ and on July 22 and 28, 2009 in the Lawrence Brook in Milltown, NJ. The two systems were installed 2 meters apart laterally across the stream to measure SOD simultaneously. A total of 7 chamber measurements and 50 profile measurements were collected over 3 days. Chamber SOD measurements in the Lawrence Brook varied from 3.6 to 13.0 g/m2/day and had a mean of 5.0 g/m2/day. Concurrent profile SOD measurements varied from 1.3 to 13.5 g/m2/day and had a mean of 7.16 g/m2/day. In the Millstone River, the single chamber measurement was 4.6 g/m2/day while the profile measurements varied from 0.5 to 2.2 g/m2/day with a mean of 1.32 g/m2/day. The measurements made via the profile and chamber methods were found to be in relative agreement. A linear relationship between friction velocity and stream SOD was observed.

Design, Construction, and Calibration of a Portable Boundary Layer Wind Tunnel for Field Use

Wind erosion is a natural process that has formed landscapes but threatens sustainable agriculture in many locations. Wind tunnels have been used for several decades to study wind erosion processes. Portable wind tunnels offer the advantage of testing natural surfaces in the field, but they must be carefully designed to ensure that a logarithmic boundary layer is formed and that wind erosion processes may develop without interference from the tunnel structures. Although large portable tunnels often meet the aerodynamic criteria, their size and transportation requirements often limit the locations where they may be employed. We designed and built a self-contained portable wind tunnel that is easily transported on a tandem-axle trailer and pulled with a pickup truck. The wind tunnel uses a centrifugal blower, a flow-conditioning section with optional abrader material feed, and a 1 m tall and 0.5 m wide working section that can vary in length from 2 m to 6 m. The maximum wind velocity attainable is 18.7 m s-1 although a mid-height centerline velocity of 12.6 m s-1 is normally used for field testing of natural surfaces. Based on measured wind velocity profiles in the tunnel working section, a conservative estimate of boundary layer depth within the working section is 0.5 m. Even though no wind tunnel can truly duplicate the scale and variability of the forces that drive wind erosion, tunnels such as this one with deeply developed boundary layers offer reasonable estimates of dust emissions and erodibilities of natural surfaces. This wind tunnel has been used to test rangeland and cropped surfaces in several locations and has provided reliable and useable soil erodibility and dust emission data.

Microsensor for in situ flow measurements in benthic boundary layers at submillimeter resolution with extremely slow flow

The currents in the lowest few millimeters of the bottom boundary layer of lakes are highly important for the dissipation of kinetic energy and for chemical processes such as oxygen transfer into the sediment. So far, no high‐resolution flow velocity profiles close to the sediment‐water interface have been reported for such systems because a suitable flow meter was lacking. This article introduces a novel sensor for the measurement of extremely low‐flow velocities. The sensor is based on a gas transducer surrounded by a gas reservoir. It measures the change in the partial pressure of a tracer gas outside the reservoir tip due to advective transport. The sensor is suitable for measurements of velocities smaller than 1 mm s−1, with a spatial resolution of 100 to 250 µm. The flow measurements prove to be insensitive to temperature changes between 5 and 15 °C. The sensor is robust against relative pressure changes, and angular differences in the sensitivity can be calibrated. We present high‐resolution in situ measurements at the bottom of a pre‐alpine lake with shear velocities as low as 0.13 ± 0.02 cm s−1. The velocity profile nicely resolves the transition zone between the viscous and the logarithmic boundary layer.

Snow saltation threshold measurements in a drifting-snow wind tunnel

AbstractWind tunnel measurements of snowdrift in a turbulent, logarithmic velocity boundary layer have been made in Davos, Switzerland, using natural snow. Regression analysis gives the drift threshold friction velocity (u*t), assuming an exponential drift profile and a simple drift to friction velocity relationship. Measurements over 15 snow covers show that u*t is influenced more by snow density and particle size than by ambient temperature and humidity, and varies from 0.27 to 0.69 ms–1. Schmidt’s threshold algorithm and a modified version used in SNOWPACK (a snow-cover model) agree well with observations if small bond sizes are assumed. Using particle hydraulic diameters, obtained from image processing, Bagnold’s threshold parameter is 0.18. Roughness lengths (z0) vary between snow covers but are constant until the start of drift. Threshold roughness lengths are proportional to . The influence of macroscopic objects on the roughness length is shown by the lower values measured over the smooth and flat snow surface of the wind tunnel (0.04 ≤ z0 ≤ 0.13 mm), compared to field measurements. Mean drifting-snow grain sizes for mainly new and partly decomposed snow are 100–175 μm, and independent of surface particle size.

Addendum to `Wind Stress Over Waves: Effects of Sea Roughness and Atmospheric Stability’

Addendum to `Wind Stress Over Waves: Effects of Sea Roughness and Atmospheric Stability’

Wind Stress Over Waves: Effects of Sea Roughness and Atmospheric Stability

The paper considers the effects of sea roughness and atmospheric stability on the sea surface wind stress over waves, which are in local equilibrium with the wind, by using the logarithmic boundary layer profile including a stability function, as well as adopting some commonly used sea surface roughness formulations. The engineering relevance of the results is also discussed.

Effects of sea roughness and atmospheric stability on wind wave growth

The paper considers the effects of sea roughness and atmospheric stability on the wind wave growth by using the logarithmic boundary layer profile including a stability function, as well as adopting Toba et al.'s [J. Phys. Ocean. 34 (1990) 705] significant wave height formula combined with some commonly used sea surface roughness formulations. The wind wave growth is represented by the non-dimensional total wave energy relative to that for neutral stability used by Young [Coast. Engng 34 (1998) 23]. For a given velocity at the 10 m elevation, spectral peak period and stability parameter, the wind wave growth is determined.