Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity

2013 ◽  
Vol 733 ◽  
pp. 558-587 ◽  
Author(s):  
Xin Guo ◽  
Lian Shen
Keyword(s):  
Surface Wave ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Direction ◽  
Stokes Drift ◽  
Mechanistic Study ◽  
Velocity Spectrum ◽  
Surface Boundary ◽  
Mean Flow ◽  
Random Forcing

AbstractDirect numerical simulation is performed to study the effect of progressive gravity waves on turbulence underneath. The Navier–Stokes equations subject to fully nonlinear kinematic and dynamic free-surface boundary conditions are simulated on a surface-following mapped grid using a fractional-step scheme with a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. To facilitate a mechanistic study that focuses on the fundamental physics of wave–turbulence interaction, the wave and turbulence fields are set up precisely in the simulation: a pressure-forcing method is used to generate and maintain the progressive wave being investigated and to suppress other wave components, and a random forcing method is used to produce statistically steady, homogeneous turbulence in the bulk flow beneath the surface wave. Cases with various moderate-to-large turbulence-to-wave time ratios and wave steepnesses are considered. Study of the turbulence velocity spectrum shows that the turbulence is dynamically forced by the surface wave. Mean flow and turbulence vorticity are studied in both the Eulerian and Lagrangian frames of the wave. In the Eulerian frame, statistics of the underlying turbulence field indicates that the magnitude of turbulence vorticity and the inclination angle of vortices are dependent on the wave phase. In the Lagrangian frame, wave properties and the accumulative effect on turbulence vorticity are studied. It is shown that vertical vortices are tilted in the wave propagation direction due to the cumulative effects of both the Stokes drift velocity and the correlation between turbulence fluctuations and wave strain rate, whereas for streamwise vortices, these two factors offset each other and result in a negligible tilting effect.

Mechanistic Study of Upper Ocean Turbulence Interacting With Surface Waves

2010 ◽  
Author(s):  
Xin Guo ◽  
Di Yang ◽  
Yi Liu ◽  
Lian Shen
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Mechanistic Study ◽  
Navier Stokes Equations ◽  
Random Forcing ◽  
Set Up ◽  
Pseudo Spectral Method

We perform direct numerical simulations to simulate the interaction between surface waves and the turbulence underneath. The Navier–Stokes equations are simulated using a pseudo-spectral method in horizontal directions and a finite-difference method in vertical direction, with fully nonlinear viscous free-surface kinematic and dynamic boundary conditions at the free surface. We set up the turbulence and the waves by a random forcing method in the bulk flow and a pressure forcing method at the surface, which were recently developed by [1]. It is found that there are surface waves generated on the free surface due to the excitation by the turbulence. The surface elevation is sensitive to the effect of gravity and surface tension. In the presence of progressive waves at the free surface, the turbulent vortical structure is turned, stretched, and compressed periodically by the strain field of waves.

Turbulent diffusion near a free surface

2000 ◽  
Vol 407 ◽  
pp. 145-166 ◽  
Author(s):  
LIAN SHEN ◽  
GEORGE S. TRIANTAFYLLOU ◽  
DICK K. P. YUE
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Turbulent Diffusion ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Numerical Study ◽  
Turbulent Shear ◽  
Surface Boundary ◽  
Mean Flow ◽  
The Mean

We study numerically and analytically the turbulent diffusion characteristics in a low-Froude-number turbulent shear flow beneath a free surface. In the numerical study, the Navier–Stokes equations are solved directly subject to viscous boundary conditions at the free surface. From an ensemble of such simulations, we find that a boundary layer develops at the free surface characterized by a fast reduction in the value of the eddy viscosity. As the free surface is approached, the magnitude of the mean shear initially increases over the boundary (outer) layer, reaches a maximum and then drops to zero inside a much thinner inner layer. To understand and model this behaviour, we derive an analytical similarity solution for the mean flow. This solution predicts well the shape and the time-scaling behaviour of the mean flow obtained in the direct simulations. The theoretical solution is then used to derive scaling relations for the thickness of the inner and outer layers. Based on this similarity solution, we propose a free-surface function model for large-eddy simulations of free-surface turbulence. This new model correctly accounts for the variations of the Smagorinsky coefficient over the free-surface boundary layer and is validated in both a priori and a posteriori tests.

scholarly journals Adjoint-based parametric sensitivity analysis for swirling M-flames

2018 ◽  
Vol 859 ◽  
pp. 516-542 ◽  
Author(s):  
Calum S. Skene ◽  
Peter J. Schmid
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computational Cost ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Perturbation Expansions ◽  
Mean Flow ◽  
Adjoint Solutions

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

scholarly journals RIP CURRENTS ON A BARRED BEACH

2012 ◽  
Vol 1 (33) ◽  
pp. 38
Author(s):  
Andrea Ruju ◽  
Pablo Higuera ◽  
Javier L. Lara ◽  
Inigo J. Losada ◽  
Giovanni Coco
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Wave Generation ◽  
Dimensional Structure ◽  
Navier Stokes ◽  
Rip Currents ◽  
Mean Flow ◽  
Forcing Mechanisms

This work presents the numerical study of rip current circulation on a barred beach. The numerical simulations have been carried out with the IH-FOAM model which is based on the three dimensional Reynolds Averaged Navier-Stokes equations. The new boundary conditions implemented in IH-FOAM have been used, including three dimensional wave generation as well as active wave absorption at the boundary. Applying the specific wave generation boundary conditions, the model is validated to simulate rip circulation on a barred beach. Moreover, this study addresses the identification of the forcing mechanisms and the three dimensional structure of the mean flow.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

1999 ◽  
Vol 122 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Robert E. Spall ◽  
Blake M. Ashby
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]

On Langmuir circulation in shallow waters

2014 ◽  
Vol 743 ◽  
pp. 141-169 ◽  
Author(s):  
W. R. C. Phillips ◽  
A. Dai
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Time Scale ◽  
Mean Field ◽  
Stokes Drift ◽  
Surface Boundary ◽  
Langmuir Circulation ◽  
Mean Flow ◽  
Mean Field Equations ◽  
Pressure Driven

AbstractThe instability of shallow-water waves on a moderate shear to Langmuir circulation is considered. In such instances, specifically at the shallow end of the inner coastal region, the shear can significantly affect the drift giving rise to profiles markedly different from the simple Stokes drift. Since drift and shear are instrumental in the instability to Langmuir circulation, of key interest is how that variation in turn affects onset to Langmuir circulation. Also of interest is the effect on onset of various boundary conditions. To that end the initial value problem describing the wave–mean flow interaction which accounts for the multiple time scales of the surface waves, evolving shear and evolving Langmuir circulation is crafted from scratch, and includes the wave-induced drift and a consistent set of free-surface boundary conditions. The problem necessitates that Navier–Stokes be employed side by side with a set of mean-field equations. Specifically, the former is used to evaluate events with the shortest time scale, that is the wave field, while the mean field set is averaged over that time scale. This averaged set, the CLg equations, follow from the generalized Lagrangian mean equations and for the case at hand take the same form as the well-known CL equations, albeit with different time and velocity scales. Results based upon the Stokes drift are used as a reference to which those based upon drift profiles corrected for shear are compared, noting that the latter are asymptotic to the former as the waves transition from shallow to deep. Two typical temporal flow fields are considered: shear-driven flow and pressure-driven flow. Relative to the reference case, shear-driven flow is found to be destabilizing while pressure driven are stabilizing to Langmuir circulation. In pressure-driven flows it is further found that multiple layers, as opposed to a single layer, of Langmuir circulation can form, with the most intense circulations at the ocean floor. Moreover, the layers can extend into a region of flow beyond that in which the instability applies, suggesting that Langmuir circulation excited by the instability can in turn drive, as a dynamic consequence, contiguous albeit less intense Langmuir circulation. Pressure-driven flows also admit two preferred spacings, one closely in accord with observation for small-aspect-ratio Langmuir circulation, the other well in excess of observed large-aspect-ratio Langmuir circulation.

scholarly journals Numerical Study of Violent Impact Flow Using a CIP-Based Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qiao-ling Ji ◽  
Xi-zeng Zhao ◽  
Sheng Dong
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Large Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Small Scale ◽  
Surface Boundary ◽  
Two Phase ◽  
Constrained Interpolation

A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Results of another two free surface capturing methods, the original VOF and CIP, are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two-dimensional (2D) and three-dimensional (3D) full scale simulations and a large-scale 2D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

Interaction of a deformable free surface with statistically steady homogeneous turbulence

2010 ◽  
Vol 658 ◽  
pp. 33-62 ◽  
Author(s):  
XIN GUO ◽  
LIAN SHEN
Keyword(s):  
Free Surface ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Pseudospectral Method ◽  
Vertical Direction ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.

scholarly journals A Quasi-Eulerian, Quasi-Lagrangian View of Surface-Wave-Induced Flow in the Ocean

2008 ◽  
Vol 38 (5) ◽  
pp. 1122-1130 ◽  
Author(s):  
Göran Broström ◽  
Kai Håkon Christensen ◽  
Jan Erik H. Weber
Keyword(s):  
Surface Wave ◽  
Vertical Direction ◽  
Momentum Balance ◽  
Material Surface ◽  
Mean Flow ◽  
Vertical Coordinate ◽  
Induced Flow ◽  
The Mean ◽  
Wave Induced ◽  
Nonuniform Wave

Abstract In this study the influence of surface waves on the mean flow in an ocean of arbitrary depth is examined. The wave-induced forcing on the mean flow is obtained by integrating the Eulerian equations for mass and momentum balance from the bottom to an undulating material surface within the water column. By using the mean position of the material surface as the vertical coordinate, the authors obtain the depth dependence of the mean flow and the wave-induced forcing. Substitution of the vertical coordinate makes the model Lagrangian in the vertical direction. The model is Eulerian in the horizontal direction, allowing one to model the effects of a spatially nonuniform wave field or varying depth in a straightforward way.

scholarly journals Development of the Physics–Based Morphology Model as the Platform for the Optimal Design of Beach Nourishment Project: A Numerical Study

2020 ◽  
Vol 8 (10) ◽  
pp. 828
Author(s):  
Yong Jun Cho
Keyword(s):  
Numerical Simulation ◽  
Optimal Design ◽  
Numerical Study ◽  
Beach Nourishment ◽  
Suspended Load ◽  
Stokes Drift ◽  
Physical Model Test ◽  
Surface Boundary ◽  
Flat Bottom ◽  
Morphology Model

In this study, a physics-based morphology model is developed and to test the feasibility of the morphology model proposed in this study as the platform for the optimal design of the beach nourishment project, the beach restoration process by the infra-gravity waves underlying the swells in a mild sea is numerically simulated. As a hydrodynamic module, the IHFOAM wave toolbox having its roots in the OpenFoam is used. Speaking of the morphology model, a transport equation for suspended load and the Exner type equation constitute the morphology model. In doing so, the probability theory first introduced by Einstein and the physical model test by Bagnold are used as the constituent sub-model of the morphology model. Numerical results show that among many flow features that are indispensable in forming sand bars over the flat bottom and swash zone, the partially skewed and asymmetric bottom shearing stresses, a shoreward Stokes drift near the free surface, boundary layer streaming near the seabed, and undertow toward the offshore were successfully simulated using the morphology model proposed in this study. It was also shown that plunging type breaker occurring at the final stage of the shoaling process, and its accompanying second breaker, sediment entrainment at the seabed, and the redistribution of suspended load by the down rush of preceding waves were successfully reproduced in the numerical simulation, and agreements with our experience in the field were very encouraging. In particular, the sand bar formation process over the flat bottom and backshore were successfully reproduced in the numerical simulation, which has been regarded as a challenging task.

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