scholarly journals On the distortion of turbulence by a progressive surface wave

2002 ◽  
Vol 458 ◽  
pp. 229-267 ◽  
Author(s):  
M. A. C. TEIXEIRA ◽  
S. E. BELCHER

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when ‘streaky structures’ of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity.The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976).The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

2019 ◽  
Vol 49 (9) ◽  
pp. 2323-2336
Author(s):  
Juan M. Restrepo ◽  
Jorge M. Ramirez

AbstractMaking use of a Lagrangian description, we interpret the kinematics and analyze the mean transport due to numerically generated transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced, air–water, two-phase Navier–Stokes solver. These transient waves produce transient transport, which can sometimes be larger than what would be estimated using estimates developed for translationally invariant progressive waves. We identify the critical assumption that makes our standard notion of the steady Stokes drift inapplicable to the data and explain how and in what sense the transport due to transient waves can be larger than the steady counterpart. A comprehensive analysis of the data in the Lagrangian framework leads us to conclude that much of the transport can be understood using an irrotational approximation of the velocity, even though the simulations use Navier–Stokes fluid simulations with moderately high Reynolds numbers. Armed with this understanding, it is possible to formulate a simple Lagrangian model that captures the mean transport and variance of transport for a large range of wave amplitudes. For large-amplitude waves, the parcel paths in the neighborhood of the free surface exhibit increased dispersion and lingering transport due to the generation of vorticity. We examined the wave-breaking case. For this case, it is possible to characterize the transport very well, away from the wave boundary layer, and approximately using a simple model that captures the unresolved breaking dynamics via a stochastic parameterization.


1992 ◽  
Vol 241 ◽  
pp. 503-523 ◽  
Author(s):  
D. J. Tritton

We consider turbulent shear flows in a rotating fluid, with the rotation axis parallel or antiparallel to the mean flow vorticity. It is already known that rotation such that the shear becomes cyclonic is stabilizing (with reference to the non-rotating case), whereas the opposite rotation is destabilizing for low rotation rates and restabilizing for higher. The arguments leading to and quantifying these statement are heuristic. Their status and limitations require clarification. Also, it is useful to formulate them in ways that permit direct comparison of the underlying concepts with experimental data.An extension of a displaced particle analysis, given by Tritton & Davies (1981) indicates changes with the rotation rate of the orientation of the motion directly generated by the shear/Coriolis instability occurring in the destabilized range.The ‘simplified Reynolds stress equations scheme’, proposed by Johnston, Halleen & Lezius (1972), has been reformulated in terms of two angles, representing the orientation of the principal axes of the Reynolds stress tensor (αa) and the orientation of the Reynolds stress generating processes (αb), that are approximately equal according to the scheme. The scheme necessarily fails at large rotation rates because of internal inconsistency, additional to the fact that it is inapplicable to two-dimensional turbulence. However, it has a wide range of potential applicability, which may be tested with experimental data. αa and αb have been evaluated from numerical data for homogeneous shear flow (Bertoglio 1982) and laboratory data for a wake (Witt & Joubert 1985) and a free shear layer (Bidokhti & Tritton 1992). The trends with varying rotation rate are notably similar for the three cases. There is a significant range of near equality of αa and αb. An extension of the scheme, allowing for evolution of the flow, relates to the observation of energy transfer from the turbulence to the mean flow.


2004 ◽  
Vol 34 (2) ◽  
pp. 490-504 ◽  
Author(s):  
Arne Melsom ◽  
Øyvind SÆtra

Abstract A theoretical model for the near-surface velocity profile in the presence of breaking waves is presented. Momentum is accumulated by growing waves and is released upon wave breaking. In effect, such a transition is a process involving a time-dependent surface stress acting on the mean current. In this paper, conventional theory for the Stokes drift is expanded to fourth-order accuracy in wave steepness. It is shown that the higher-order terms lead to an enhancement of the surface Stokes drift and a slight retardation of the Stokes volume flux. Furthermore, the results from the wave theory are used to obtain a bulk parameterization of momentum exchange during the process of wave breaking. The mean currents are then obtained by application of a variation of the “level 2.5” turbulence closure theory of Mellor and Yamada. When compared with the traditional approach of a constant surface stress, the mean Eulerian current exhibits a weak enhancement in the near-surface region, compensated by a negative shift deeper in the water column. However, it is found that the results of Craig and Banner and the results of Craig are not significantly affected by the present theory. Hence, this study helps to explain why the Craig and Banner model agrees well with observations when a realistic, time-varying surface stress acts on the drift currents.


1979 ◽  
Vol 93 (3) ◽  
pp. 501-513 ◽  
Author(s):  
J. N. Gence ◽  
J. Mathieu

A grid-generated turbulence is subjected to a pure plane strain and the principal axes of the Reynolds stress tensor become those of the strain. This ‘oriented’ homogeneous turbulence is then submitted to a new strain the principal axes of which have a different orientation. We show that in such a situation it is possible to observe a transfer of energy from the fluctuating motion to the mean one. Such transfer is necessarily associated with a forced decay of the anisotropy of the motion. A detailed analysis of the reorientation of the principal axes of the Reynolds stress tensor in the frame of those of the second strain gives an explanation of the evolution of the principal axes of the Reynolds stress tensor in a shear flow.


1968 ◽  
Vol 33 (1) ◽  
pp. 1-20 ◽  
Author(s):  
S. C. Crow

A number of shear-flow phenomena can be explained qualitatively if turbulence is regarded as a continuous viscoelastic medium with respect to its action on a mean field. Conditions are sought under which the analogy is quantitative, and it is found that the turbulence must be fine-grained and the mean field weak. For geometrical convenience the turbulence is assumed to be nearly homogeneous and isotropic so that body forces are required to maintain it. The turbulence is found to respond initially to an arbitrary deformation as an elastic medium, in which Reynolds stress is linearly proportional to strain. Three processes that cause the resulting Reynolds stress to relax are distinguished: viscous diffusion, body-force agitation and non-linear scrambling. It is argued that, regardless of which process dominates, Reynolds stress evolves in a continuously changing mean field according to a viscoelastic constitutive law, relating stress to deformation history by means of a scalar memory function. The argument is carried through analytically for weak turbulence, in which non-linear scrambling is negligible, and the memory function is computed in terms of the wave-number-frequency spectrum of the background turbulence. In the course of the analysis, a new type of Reynolds stress arises related to the passage of the turbulence through its sustaining environment of body forces. It is found that the mean field must be surprisingly weak for this ‘translation stress’ to be negligible. Applications of the viscoelasticity theory of turbulent shear flow are discussed in which body forces and therefore translation stress are absent.


2019 ◽  
Vol 865 ◽  
pp. 1042-1071 ◽  
Author(s):  
Nabil Abderrahaman-Elena ◽  
Chris T. Fairhall ◽  
Ricardo García-Mayoral

Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the roughness size increases, the background turbulence begins to be modified, notably by the increase of energy for short, wide wavelengths, which is consistent with the appearance of a shear-flow instability of the mean flow. A laminar model is presented to estimate the roughness-coherent contribution, as well as the displacement height and the velocity at the roughness crests. Based on the effects observed in the background turbulence, the roughness function is decomposed into different terms to analyse different contributions to the change in drag, laying the foundations for a predictive model.


1967 ◽  
Vol 27 (1) ◽  
pp. 131-144 ◽  
Author(s):  
O. M. Phillips

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence\[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where${\cal A}$is a number, Θ the convected integral time scale of thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.


2009 ◽  
Vol 639 ◽  
pp. 479-507 ◽  
Author(s):  
NIKOLAOS A. BAKAS

Non-modal mechanisms underlying transient growth of propagating acoustic waves and non-propagating vorticity perturbations in an unbounded compressible shear flow are investigated, making use of closed form solutions. Propagating acoustic waves amplify mainly due to two mechanisms: growth due to advection of streamwise velocity that is typically termed as the lift-up mechanism leading for large Mach numbers to an almost linear increase in streamwise velocity with time and growth due to the downgradient irrotational component of the Reynolds stress leading to linear growth of acoustic wave energy for large times. Synergy between these mechanisms along with the downgradient solenoidal component of the Reynolds stress produces large and robust energy amplification.On the other hand, non-propagating vorticity perturbations amplify due to kinematic deformation of vorticity by the mean flow. For weakly compressible flows, an initial vorticity perturbation abruptly excites acoustic waves with exponentially small amplitude, and the energy gained by vorticity perturbations is transferred back to the mean flow. For moderate Mach numbers, a strong coupling between vorticity perturbations and acoustic waves is found with the energy gained by vorticity perturbations being transferred to acoustic waves that are abruptly excited by the vortex.Calculation of the optimal perturbations for a viscous flow shows that for low Mach numbers, acoustic wave excitation by vorticity perturbations and the subsequent growth of acoustic waves leads to robust energy growth of the order of Reynolds number, while for large Mach numbers, synergy between the lift-up mechanism and the downgradient solenoidal component of the Reynolds stress dominates the growth and leads to a comparable large amplification of streamwise velocity.


2020 ◽  
pp. 34-42
Author(s):  
Thibault Chastel ◽  
Kevin Botten ◽  
Nathalie Durand ◽  
Nicole Goutal

Seagrass meadows are essential for protection of coastal erosion by damping wave and stabilizing the seabed. Seagrass are considered as a source of water resistance which modifies strongly the wave dynamics. As a part of EDF R & D seagrass restoration project in the Berre lagoon, we quantify the wave attenuation due to artificial vegetation distributed in a flume. Experiments have been conducted at Saint-Venant Hydraulics Laboratory wave flume (Chatou, France). We measure the wave damping with 13 resistive waves gauges along a distance L = 22.5 m for the “low” density and L = 12.15 m for the “high” density of vegetation mimics. A JONSWAP spectrum is used for the generation of irregular waves with significant wave height Hs ranging from 0.10 to 0.23 m and peak period Tp ranging from 1 to 3 s. Artificial vegetation is a model of Posidonia oceanica seagrass species represented by slightly flexible polypropylene shoots with 8 artificial leaves of 0.28 and 0.16 m height. Different hydrodynamics conditions (Hs, Tp, water depth hw) and geometrical parameters (submergence ratio α, shoot density N) have been tested to see their influence on wave attenuation. For a high submergence ratio (typically 0.7), the wave attenuation can reach 67% of the incident wave height whereas for a low submergence ratio (< 0.2) the wave attenuation is negligible. From each experiment, a bulk drag coefficient has been extracted following the energy dissipation model for irregular non-breaking waves developed by Mendez and Losada (2004). This model, based on the assumption that the energy loss over the species meadow is essentially due to the drag force, takes into account both wave and vegetation parameter. Finally, we found an empirical relationship for Cd depending on 2 dimensionless parameters: the Reynolds and Keulegan-Carpenter numbers. These relationships are compared with other similar studies.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1563.3-1563
Author(s):  
H. Tamaki ◽  
S. Fukui ◽  
T. Nakai ◽  
G. Kidoguchi ◽  
S. Kawaai ◽  
...  

Background:Currently it is hypothesized that many systemic autoimmune diseases occur due to environmental risk factors in addition to genetic risk factors. Anti-Neutrophil Cytoplasmic Antibody (ANCA) is mainly associated with three systemic autoimmune disease including granulomatosis with polyangiitis (GPA), microscopic polyangiitis (MPA), eosinophilic granulomatosis with polyangiitis (EGPA). It is known that ANCA can be positive before clinical symptoms in patients with known diagnosis of GPA and ANCA titers rise before clinical manifestations appear. However, prevalence of ANCA among general population is not well known. It has not been described as well how many of people with positive ANCA eventually develop clinical manifestations of ANCA associated Vasculitis.Objectives:This study aims to estimate prevalence of ANCA in general population without ANCA associated Vasculitis. It also describes natural disease course of people with positive ANCA without ANCA associated Vasculitis. Risk factors for positive ANCA are also analyzed.Methods:This is a single center retrospective study at Center for Preventive Medicine of St. Luke’s International Hospital in Tokyo. ANCA was checked among the patients who wished to between 2018 and 2019. St. Luke’s Health Check-up Database (SLHCD) was utilized to collect the data. The patients whose serum was measured for ANCA were identified. The data for basic demographics, social habits, dietary habits and laboratory data were extracted. The charts of the patients with positive ANCA were reviewed.Results:Sera of total 1204 people were checked for ANCA. Of these 1204 people, 587 (48.8%) are male and the mean age was 55.8 years (32.6 to 79). There were total 11 patients with positive ANCA. Myeloperoxidase ANCA (MPO-ANCA) was positive for 3 patients and proteinase 3 ANCA (PR3-ANCA) was positive for 8 patients. Of these 11 patients, 5 were male (45.5%) and the mean age was 54.6 years. Two patients had history of autoimmune disease (primary biliary cirrhosis and ulcerative colitis). Five patients were evaluated by rheumatologists with the median follow-up period of 274 days. None of them developed clinical signs and symptoms of ANCA associated Vasculitis. Four out of five patients had ANCA checked later, two of which turned negative. The prevalence of ANCA in this cohort was 0.9% (95% confidence interval [95% CI]: 0.5% to 1.6%). Univariate analysis was performed to identify risk factors of positive ANCA. The variables analyzed include age, gender, body mass index (BMI), smoking habits, alcohol intake, dietary habits (fruits, fish, red meat), hypertension, dyslipidemia, and laboratory data. None of these variables demonstrated statistically significant differences except for positive rheumatoid factor (ANCA positive group: 33 % vs ANCA negative group: 9.1%, p value = 0.044).Conclusion:The prevalence of ANCA in this cohort was 0.9% (95% CI: 0.5% to 1.6%). None of them who had a follow-up developed ANCA associated Vasculitis during the follow-up period. Longer follow-up and more patients are necessary to determine natural course of people with positive ANCA.Disclosure of Interests:None declared


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