scholarly journals Mean Current Profile over Rippled-Beds in the Presence of Non-Breaking Waves and Analysis of Its Influencing Factors

2021 ◽  
Vol 9 (9) ◽  
pp. 986
Author(s):  
Chunye Hu ◽  
Jialing Hao ◽  
Zhen Liu
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Thickness ◽  
Eddy Viscosity ◽  
Present Model ◽  
Breaking Waves ◽  
The Mean ◽  
Rippled Beds ◽  
Wave Induced ◽  
Wave Boundary ◽  
Mean Current

Classical eddy viscosity model deviates from the actual mean current profiles, when calculating the mean current profiles over rippled-beds in the presence of non-breaking waves, owing to the neglect of the enhancement of the wave boundary layer thickness by ripples and the wave-induced shear stress (the radiation stress and the wave Reynolds stress). Considering these shortcomings, a semi-empirical one-dimensional vertical (1DV) model is presented in this study. The present model was obtained using the two-dimensional Navier–Stokes equations and eddy viscosity assumptions, which differ from those of previous researchers, while a top-to-bottom sequence was adopted to calculate the mean current profiles. Empirical formulae were derived from the laboratory measurements and used in the present model to accurately predict the wave boundary layer thickness and bed roughness. The present model is in satisfactory agreement with the data from laboratory experiments. The factors influencing the mean current profiles were analyzed also. The wave-induced second-order shear stresses were found to be the principal reason for the deviations of the mean current profiles in the near-surface layer; as the influencing factors of wave-induced shear stress, the intensity of the wave relative to the current, the angle between the wave and current, and the size of ripples can also have a non-negligible effect on the mean current profiles.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Experimental study of the mean structure and quasi-conical scaling of a swept-compression-ramp interaction at Mach 2

2018 ◽  
Vol 841 ◽  
pp. 1-27 ◽  
Author(s):  
Leon Vanstone ◽  
Mustafa Nail Musta ◽  
Serdar Seckin ◽  
Noel Clemens
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Particle Image Velocimetry ◽  
Flow Field ◽  
Scaling Laws ◽  
Particle Image ◽  
Separated Flow ◽  
Image Velocimetry ◽  
The Mean ◽  
Wave Boundary

This study investigates the mean flow structure of two shock-wave boundary-layer interactions generated by moderately swept compression ramps in a Mach 2 flow. The ramps have a compression angle of either $19^{\circ }$ or $22.5^{\circ }$ and a sweep angle of $30^{\circ }$. The primary diagnostic methods used for this study are surface-streakline flow visualization and particle image velocimetry. The shock-wave boundary-layer interactions are shown to be quasi-conical, with the intermittent region, separation line and reattachment line all scaling in a self-similar manner outside of the inception region. This is one of the first studies to investigate the flow field of a swept ramp using particle image velocimetry, allowing more sensitive measurements of the velocity flow field than previously possible. It is observed that the streamwise velocity component outside of the separated flow reaches the quasi-conical state at the same time as the bulk surface flow features. However, the streamwise and cross-stream components within the separated flow take longer to recover to the quasi-conical state, which indicates that the inception region for these low-magnitude velocity components is actually larger than was previously assumed. Specific scaling laws reported previously in the literature are also investigated and the results of this study are shown to scale similarly to these related interactions. Certain limiting cases of the scaling laws are explored that have potential implications for the interpretation of cylindrical and quasi-conical scaling.

Numerical Modeling of Turbulent Wall-Bounded Oscillatory Flow and its Effect on Small-Diameter Pipelines

2020 ◽  
Author(s):  
Hongyi Jiang ◽  
Liang Cheng
Keyword(s):  
Boundary Layer ◽  
Oscillatory Flow ◽  
Small Diameter ◽  
Viscous Sublayer ◽  
Theoretical Estimation ◽  
Wall Boundary Condition ◽  
Mesh Resolution ◽  
Turbulent Wall ◽  
Wave Induced ◽  
Wave Boundary

Abstract This study investigates the effect of wave-induced boundary layer on the on-bottom stability of small-diameter pipelines laid on the seabed. An ω-based wall boundary condition is adopted, owing to its high mesh resolution down to the viscous sublayer to resolve the flow around the pipeline. By taking into account the wave boundary layer, the present numerical simulations predict required specific gravity for small-diameter pipelines close to the theoretical estimation by Cheng et al. (2016) and, as expected, much smaller than those recommended by DNV-RP-F109.

scholarly journals Winds near the Surface of Waves: Observations and Modeling

2018 ◽  
Vol 48 (5) ◽  
pp. 1079-1088 ◽  
Author(s):  
Alexander V. Babanin ◽  
Jason McConochie ◽  
Dmitry Chalikov
Keyword(s):  
Boundary Layer ◽  
Wind Wave ◽  
Wave Boundary Layer ◽  
Wind Speeds ◽  
Vertical Profiling ◽  
The Mean ◽  
Flux Layer ◽  
Logarithmic Layer ◽  
Wave Boundary ◽  
Lake George

AbstractThe concept of a constant-flux layer is usually employed for vertical profiling of the wind measured at some elevation near the ocean surface. The surface waves, however, modify the balance of turbulent stresses very near the surface, and therefore such extrapolations can introduce significant biases. This is particularly true for buoy measurements in extreme conditions, when the anemometer mast is within the wave boundary layer (WBL) or even below the wave crests. In this paper, field data and a WBL model are used to investigate such biases. It is shown that near the surface the turbulent stresses are less than those obtained by extrapolation using the logarithmic-layer assumption, and the mean wind speeds very near the surface, based on Lake George field observations, are up to 5% larger. The behavior is then simulated by means of a WBL model coupled with nonlinear waves, which confirmed the observations and revealed further details of complex behaviors at the wind-wave boundary layer.

scholarly journals The Role of Wave-Induced Coriolis–Stokes Forcing on the Wind-Driven Mixed Layer

2005 ◽  
Vol 35 (4) ◽  
pp. 444-457 ◽  
Author(s):  
Jeff A. Polton ◽  
David M. Lewis ◽  
Stephen E. Belcher
Keyword(s):  
Analytical Solution ◽  
Observational Data ◽  
Mixed Layer ◽  
Analytical Solutions ◽  
Eddy Viscosity ◽  
Large Eddy Simulations ◽  
Current Profile ◽  
Large Eddy ◽  
The Mean ◽  
Mean Current

Abstract The interaction between the Coriolis force and the Stokes drift associated with ocean surface waves leads to a vertical transport of momentum, which can be expressed as a force on the mean momentum equation in the direction along wave crests. How this Coriolis–Stokes forcing affects the mean current profile in a wind-driven mixed layer is investigated using simple models, results from large-eddy simulations, and observational data. The effects of the Coriolis–Stokes forcing on the mean current profile are examined by reappraising analytical solutions to the Ekman model that include the Coriolis–Stokes forcing. Turbulent momentum transfer is modeled using an eddy-viscosity model, first with a constant viscosity and second with a linearly varying eddy viscosity. Although the Coriolis–Stokes forcing penetrates only a small fraction of the depth of the wind-driven layer for parameter values typical of the ocean, the analytical solutions show how the current profile is substantially changed through the whole depth of the wind-driven layer. It is shown how, for this oceanic regime, the Coriolis–Stokes forcing supports a fraction of the applied wind stress, changing the boundary condition on the wind-driven component of the flow and hence changing the current profile through all depths. The analytical solution with the linearly varying eddy viscosity is shown to reproduce reasonably well the effects of the Coriolis–Stokes forcing on the current profile computed from large-eddy simulations, which resolve the three-dimensional overturning motions associated with the turbulent Langmuir circulations in the wind-driven layer. Last, the analytical solution with the Coriolis–Stokes forcing is shown to agree reasonably well with current profiles from previously published observational data and certainly agrees better than the standard Ekman model. This finding provides evidence that the Coriolis–Stokes forcing is an important mechanism in controlling the dynamics of the upper ocean.

A model for inhomogeneous turbulent flow

1970 ◽  
Vol 317 (1530) ◽  
pp. 417-433 ◽  
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
The Self ◽  
Diffusion Equations ◽  
Mean Flow ◽  
Mean Velocity ◽  
Closed Set ◽  
Law Of The Wall ◽  
The Mean ◽  
Model Equations

A set of model equations is given to describe the gross features of a statistically steady or 'slowly varying’ inhomogeneous field of turbulence and the mean velocity distribution. The equations are based on the idea that turbulence can be characterized by ‘densities’ which obey nonlinear diffusion equations. The diffusion equations contain terms to describe the convection by the mean flow, the amplification due to interaction with a mean velocity gradient, the dissipation due to the interaction of the turbulence with itself, and the dif­fusion also due to the self interaction. The equations are similar to a set proposed by Kolmo­gorov (1942). It is assumed that both an ‘energy density’ and a ‘vorticity density’ satisfy diffusion equations, and that the self diffusion is described by an eddy viscosity which is a function of the energy and vorticity densities; the eddy viscosity is also assumed to describe the diffu­sion of mean momentum by the turbulent fluctuations. It is shown that with simple and plausible assumptions about the nature of the interaction terms, the equations form a closed set. The appropriate boundary conditions at a solid wall and a turbulent interface, with and without entrainment, are discussed. It is shown that the dimensionless constants which appear in the equations can all be estimated by general arguments. The equations are then found to predict the von Kármán constant in the law of the wall with reasonable accuracy. An analytical solution is given for Couette flow, and the result of a numerical study of plane Poiseuille flow is described. The equations are also applied to free turbulent flows. It is shown that the model equations completely determine the structure of the similarity solutions, with the rate of spread, for instance, determined by the solution of a nonlinear eigenvalue problem. Numerical solutions have been obtained for the two-dimensional wake and jet. The agreement with experiment is good. The solutions have a sharp interface between turbulent and non-turbulent regions and the mean velocity in the turbulent part varies linearly with distance from the interface. The equations are applied qualitatively to the accelerating boundary layer in flow towards a line sink, and the decelerating boundary layer with zero skin friction. In the latter case, the equations predict that the mean velocity should vary near the wall like the 5/3 power of the distance. It is shown that viscosity can be incorporated formally into the model equations and that a structure can be given to the interface between turbulent and non-turbulent parts of the flow.

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