scholarly journals Turbulent transition in a truncated one-dimensional model for shear flow

2011 ◽  
Vol 467 (2135) ◽  
pp. 3066-3087 ◽  
Author(s):  
J. H. P. Dawes ◽  
W. J. Giles
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Turbulent Flows ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Initial Perturbation ◽  
Initial Energy ◽  
Chaotic Regime ◽  
Transition To Turbulence ◽  
Spanwise Direction

We present a reduced model for the transition to turbulence in shear flow that is simple enough to admit a thorough numerical investigation, while allowing spatio-temporal dynamics that are substantially more complex than those allowed in previous modal truncations. Our model allows a comparison of the dynamics resulting from initial perturbations that are localized in the spanwise direction with those resulting from sinusoidal perturbations. For spanwise-localized initial conditions, the subcritical transition to a ‘turbulent’ state (i) takes place more abruptly, with a boundary between laminar and turbulent flows that appears to be much less ‘structured’ and (ii) results in a spatio-temporally chaotic regime within which the lifetimes of spatio-temporally complicated transients are longer, and are even more sensitive to initial conditions. The minimum initial energy E 0 required for a spanwise-localized initial perturbation to excite a chaotic transient has a power-law scaling with the Reynolds number E 0 ∼ Re p with p ≈−4.3. The exponent p depends only weakly on the width of the localized perturbation and is lower than that commonly observed in previous low-dimensional models where typically p ≈−2. The distributions of lifetimes of chaotic transients at the fixed Reynolds number are found to be consistent with exponential distributions.

Common features between the Newtonian laminar–turbulent transition and the viscoelastic drag-reducing turbulence

2019 ◽  
Vol 877 ◽  
pp. 405-428 ◽  
Author(s):  
Anselmo S. Pereira ◽  
Roney L. Thompson ◽  
Gilmar Mompean
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Turbulent Flows ◽  
Temporal Dynamics ◽  
Homoclinic Orbits ◽  
Theoretical Development ◽  
Transitional Flows ◽  
Turbulent Transition ◽  
Laminar Turbulent Transition

The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of Reynolds (Phil. Trans. R. Soc. Lond. A, vol. 174, 1883, pp. 935–982). Recently, experimental and numerical investigations on this matter have demonstrated that the spatio-temporal dynamics that are associated with transitional flows belong to the directed percolation class. In the present work, we explore the analysis of laminar–turbulent transition from the perspective of the recent theoretical development that concerns viscoelastic turbulence, i.e. the drag-reducing turbulent flow obtained from adding polymers to a Newtonian fluid. We found remarkable fingerprints of the variety of states that are present in both types of flows, as captured by a series of features that are known to be present in drag-reducing viscoelastic turbulence. In particular, when compared to a Newtonian fully turbulent flow, the universal nature of these flows includes: (i) the statistical dynamics of the alternation between active and hibernating turbulence; (ii) the weakening of elliptical and hyperbolic structures; (iii) the existence of high and low drag reduction regimes with the same boundary; (iv) the relative enhancement of the streamwise-normal stress; and (v) the slope of the energy spectrum decay with respect to the wavenumber. The maximum drag reduction profile was attained in a Newtonian flow with a Reynolds number near the boundary of the laminar regime and in a hibernating state. It is generally conjectured that, as the Reynolds number increases, the dynamics of the intermittency that characterises transitional flows migrate from a situation where heteroclinic connections between the upper and the lower branches of solutions are more frequent to another where homoclinic orbits around the upper solution become the general rule.

scholarly journals Dynamics of spatially localized states in transitional plane Couette flow

2019 ◽  
Vol 867 ◽  
pp. 414-437 ◽  
Author(s):  
Anton Pershin ◽  
Cédric Beaume ◽  
Steven M. Tobias
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Localized States ◽  
Transition To Turbulence ◽  
Dynamical Structure ◽  
Plane Couette Flow ◽  
Homoclinic Snaking ◽  
Chaotic Transients

Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing homoclinic snaking (Schneider et al., Phys. Rev. Lett., vol. 104, 2010, 104501). These branches can be used to generate a number of spatially localized initial conditions whose transition can be investigated. From the low Reynolds numbers where homoclinic snaking is first observed ($Re<175$) to transitional ones ($Re\approx 325$), these spatially localized states traverse various regimes where their relaminarization time and dynamics are affected by the dynamical structure of phase space. These regimes are reported and characterized in this paper for a $4\unicode[STIX]{x03C0}$-periodic domain in the streamwise direction as a function of the two remaining variables: the Reynolds number and the width of the localized pattern. Close to the snaking, localized states are attracted by spatially localized periodic orbits before relaminarizing. At larger values of the Reynolds number, the flow enters a chaotic transient of variable duration before relaminarizing. Very long chaotic transients ($t>10^{4}$) can be observed without difficulty for relatively low values of the Reynolds number ($Re\approx 250$).

Instability and breakdown of a vertical vortex pair in a strongly stratified fluid

2008 ◽  
Vol 606 ◽  
pp. 239-273 ◽  
Author(s):  
MICHAEL L. WAITE ◽  
PIOTR K. SMOLARKIEWICZ
Keyword(s):  
Reynolds Number ◽  
Laboratory Experiments ◽  
Gravitational Instability ◽  
Initial Perturbation ◽  
Vortex Pair ◽  
Horizontal Displacement ◽  
Transition To Turbulence ◽  
Large Reynolds Number ◽  
Length Scales ◽  
Moderate Reynolds Number

The dynamics of a counter-rotating pair of columnar vortices aligned parallel to a stable density gradient are investigated. By means of numerical simulation, we extend the linear analyses and laboratory experiments of Billant & Chomaz (J. Fluid Mech. vol. 418, p. 167; vol. 419, pp. 29, 65 (2000)) to the fully nonlinear, large-Reynolds-number regime. A range of stratifications and vertical length scales is considered, with Frh < 0.2 and 0.1 < Frz < 10. Here Frh ≡ U/(NR) and Frz ≡ Ukz/N are the horizontal and vertical Froude numbers, U and R are the horizontal velocity and length scales of the vortices, N is the Brunt–Väisälä frequency, and 2π/kz is the vertical wavelength of a small initial perturbation. At early times with Frz < 1, linear predictions for the zigzag instability are reproduced. Short-wavelength perturbations with Frz > 1 are found to be unstable as well, with growth rates only slightly less than those of the zigzag instability but with very different structure. At later times, the large-Reynolds-number evolution diverges profoundly from the moderate-Reynolds-number laboratory experiments as the instabilities transition to turbulence. For the zigzag instability, this transition occurs when density perturbations generated by the vortex bending become gravitationally unstable. The resulting turbulence rapidly destroys the vortex pair. We derive the criterion η/R ≈ 0.2/Frz for the onset of gravitational instability, where η is the maximum horizontal displacement of the bent vortices, and refine it to account for a finite twisting disturbance. Our simulations agree for the fastest growing wavelengths 0.3 < Frz < 0.8. Short perturbations with Frz > 1 saturate at low amplitude, preserving the columnar structure of the vortices well after the generation of turbulence. Viscosity is shown to suppress the transition to turbulence for Reynolds number Re ≲ 80/Frh, yielding laminar dynamics and, under certain conditions, pancake vortices like those observed in the laboratory.

Mixing, entrainment and fractal dimensions of surfaces in turbulent flows

1989 ◽  
Vol 421 (1860) ◽  
pp. 79-108 ◽  
Keyword(s):  
Reynolds Number ◽  
Fractal Dimension ◽  
Shear Flow ◽  
Turbulent Flows ◽  
Fractal Dimensions ◽  
Irrotational Flow ◽  
Countercurrent Shear

Some basic thoughts are set down on the relation between the fractal dimension of various surfaces in turbulent flows, and the practically important processes of mixing between two streams (reacting or otherwise) separated by a convoluted surface, as well as of entrainment of irrotational flow by a turbulent stream. An expression based on heuristic arguments is derived for the flux of transportable properties (such as mass, momentum, and energy) across surfaces, and a prediction made on this basis for the fractal dimension of surfaces in fully turbulent flows is shown to be in essential agreement with measurements. It is further shown that this prediction remains robust when corrected for the non-uniform effects along the surface. A related prediction concerning the dependence of mixing on the Reynolds number and the fractal dimension of the surface is substantiated, in the developing as well as the fully developed states, by independent measurements of both the fractal dimension and the amount of mixing between reactants in a temporally evolving countercurrent shear flow.

Dissipation-range geometry and scalar spectra in sheared stratified turbulence

1999 ◽  
Vol 401 ◽  
pp. 209-242 ◽  
Author(s):  
WILLIAM D. SMYTH
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Turbulent Flows ◽  
Passive Scalar ◽  
Stratified Turbulence ◽  
Stratified Shear Flow ◽  
Dependent Strain ◽  
Parallel Shear Flow ◽  
High Reynolds ◽  
Dissipation Range

Direct numerical simulations of turbulence resulting from Kelvin–Helmholtz instability in stratified shear flow are used to examine the geometry of the dissipation range in a variety of flow regimes. As the buoyancy and shear Reynolds numbers that quantify the degree of isotropy in the dissipation range increase, alignment statistics evolve from those characteristic of parallel shear flow to those found previously in studies of stationary, isotropic, homogeneous turbulence (e.g. Ashurst et al. 1987; She et al. 1991; Tsinober et al. 1992). The analysis yields a limiting value for the mean compression rate of scalar gradients that is expected to be characteristic of all turbulent flows at sufficiently high Reynolds number.My main focus is the value of the constant q that appears in both the Batchelor (1959) and Kraichnan (1968) theoretical forms for the passive scalar spectrum. Taking account of the effects of time-dependent strain, I propose a revised estimate of q, denoted qe, which appears to agree with spectral shapes derived from simulations and observations better than do previous theoretical estimates. The revised estimate is qe = 7.3±4, and is expected to be valid whenever the buoyancy Reynolds number exceeds O(102). The Kraichnan (1968) spectral form, in which effects of intermittency are accounted for, provides a better fit to the DNS results than does the Batchelor (1959) form.

A Modified Turbulence Model for Low Reynolds Numbers: Application to Hydrostatic Seals

2005 ◽  
Vol 127 (1) ◽  
pp. 130-140 ◽  
Author(s):  
Noe¨l Brunetie`re
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Axial Stiffness ◽  
Low Reynolds Numbers ◽  
Order Of Magnitude ◽  
Low Reynolds ◽  
The Stability

A modification of the Elrod and Ng turbulence model is presented. The order of magnitude of the Reynolds number in thin lubricant films varies between 102 and 105. For Reynolds numbers higher than 103, the fluid flow becomes turbulent. It is well accepted in lubrication to use a zero-equation turbulence model of the type developed by Constantinescu (1962, ASME J. Basic Eng., 84(1), pp. 139–151), Ng (1964, ASLE Trans., 7, pp. 311–321), Ng and Pan (1965, ASME J. Basic Eng., 87, pp. 675–688), Elrod and Ng (1967, ASME J. Lubr. Technol., 89, pp. 346–362), or Hirs (1973, ASME J. Lubr. Technol., 95, pp. 137–146). The Elrod and Ng approach is certainly the most efficient for combined pressure and shear flows where the Reynolds number is above 104. This paper proposes a modification of the Elrod and Ng model in order to ensure a good correlation with experimental data obtained with low Reynolds number turbulent flows. The present model, coupled with a scaling factor for taking into account the transition to turbulence, is therefore accurate for all of the typical Reynolds number values recorded in lubrication. The model is then applied to hydrostatic noncontacting face seals, which usually operate at Reynolds numbers varying from 103 to 104. The accuracy of the model is shown for this particular application of radial rotating flow. A special study is made of the transition to turbulence. The results are compared with those obtained using the initial Elrod and Ng model. The axial stiffness coefficient and the stability threshold are significantly affected by the turbulence model.

scholarly journals Characteristics of the circular subsonic laminar jets flow with an initial Poiseuille profile

2021 ◽  
Vol 2119 (1) ◽  
pp. 012021
Author(s):  
V V Lemanov ◽  
V I Terekhov ◽  
K A Sharov ◽  
A A Shumeiko
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Satisfactory Agreement ◽  
Initial Conditions ◽  
Transition To Turbulence ◽  
Hot Wire ◽  
Air Jet ◽  
Laminar Jets ◽  
Jet Axis

Abstract In this work, the experimental data are compared with the version of the “strong” jet (Re ≫ 1) of the exact Landau-Squire solution. The experiments were performed for a submerged air jet flowing out of a tube with a diameter of D = 3.2 mm and a length of more than 100D at a Reynolds number equal to Re = 436. The initial conditions in the jet are the Poiseuille velocity profile, the level of velocity pulsations is less than 1%. Measurements were carried out using a hot-wire anemometer. It is shown that satisfactory agreement with theory is achieved at distances from the tube starting from x/D = 5.6 and up to the zone of transition to turbulence (x/D > 35). Turbulence along the jet axis will increase from 1% to 2.5%, while in the mixing layers it increases to 4.7%.

A Modified Turbulence Model for Low Reynolds Numbers: Applications to Hydrostatic Seals

2004 ◽  
Author(s):  
Noe¨l Brunetie`re
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Axial Stiffness ◽  
Low Reynolds Numbers ◽  
Order Of Magnitude ◽  
Low Reynolds ◽  
The Stability

The order of magnitude of the Reynolds number in thin lubricant films varies between 102 and 105. For Reynolds numbers higher than 103, the fluid flow becomes turbulent. It is well accepted in lubrication to use a zero equation turbulence model of the type developed by Constantinescu [1] or Elrod, Ng and Pan [2–4] or Hirs [5]. The Elrod and Ng approach is certainly the most efficient for combined pressure and shear flows where the Reynolds number is above 104. This paper proposes a modification of the Elrod and Ng model in order to ensure a good correlation with experimental data obtained with low Reynolds number turbulent flows. The present model, coupled with a scaling factor for taking into account the transition to turbulence, is therefore accurate for all the typical Reynolds number values recorded in lubrication. The model is then applied to hydrostatic noncontacting face seals, which usually operate at Reynolds numbers varying from 103 to 104. The accuracy of the model is shown for this particular application of radial rotating flow. A special study is made of the transition to turbulence. The results are compared with those obtained using the initial Elrod and Ng model. The axial stiffness coefficient and the stability threshold are significantly affected by the turbulence model.

Optimal growth and transition to turbulence in channel flow with spanwise magnetic field

2008 ◽  
Vol 596 ◽  
pp. 73-101 ◽  
Author(s):  
DMITRY KRASNOV ◽  
MAURICE ROSSI ◽  
OLEG ZIKANOV ◽  
THOMAS BOECK
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Strong Magnetic Field ◽  
Channel Flow ◽  
Flow Direction ◽  
Three Dimensional ◽  
Optimal Growth ◽  
Transition To Turbulence ◽  
Spanwise Direction ◽  
The Moment

Instability and transition to turbulence in a magnetohydrodynamic channel flow are studied numerically for the case of a uniform magnetic field imposed along the spanwise direction. Optimal perturbations and their maximum amplifications over finite time intervals are computed in the framework of the linear problem using an iterative scheme based on direct and adjoint governing equations. It is shown that, at sufficiently strong magnetic field, the maximum amplification is no longer provided by classical streamwise rolls, but rather by rolls oriented at an oblique angle to the basic flow direction. The angle grows with the Hartmann numberHaand reaches the limit corresponding to purely spanwise rolls atHabetween 50 and 100 depending on the Reynolds number. Direct numerical simulations are applied to investigate the transition to turbulence at a single subcritical Reynolds numberRe= 5000 and various Hartmann numbers. The transition is caused by the transient growth and subsequent breakdown of optimal perturbations, which take the form of one or two symmetric optimal modes (streamwise, oblique or spanwise modes depending onHa) with low-amplitude three-dimensional noise added at the moment of strongest energy amplification. A sufficiently strong magnetic field (Halarger than approximately 30) is found to completely suppress the instability. At smaller Hartmann numbers, the transition is observed but it is modified in comparison with the pure hydrodynamic case.

scholarly journals Simulation of Flexible Fibre Particle Interaction with a Single Cylinder

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 191
Author(s):  
Naser Hamedi ◽  
Lars-Göran Westerberg
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Fibre Orientation ◽  
Flow Direction ◽  
Particle Interaction ◽  
Orientation Angle ◽  
Factors Affecting ◽  
Single Cylinder ◽  
Flow Past ◽  
Fibre Suspension

In the present study, the flow of a fibre suspension in a channel containing a cylinder was numerically studied for a very low Reynolds number. Further, the model was validated against previous studies by observing the flexible fibres in the shear flow. The model was employed to simulate the rigid, semi-flexible, and fully flexible fibre particle in the flow past a single cylinder. Two different fibre lengths with various flexibilities were applied in the simulations, while the initial orientation angle to the flow direction was changed between 45° ≤ θ ≤ 75°. It was shown that the influence of the fibre orientation was more significant for the larger orientation angle. The results highlighted the influence of several factors affecting the fibre particle in the flow past the cylinder.

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