scholarly journals Universal continuous transition to turbulence in a planar shear flow

2017 ◽  
Vol 824 ◽  
Author(s):  
Matthew Chantry ◽  
Laurette S. Tuckerman ◽  
Dwight Barkley
Keyword(s):  
Shear Flow ◽  
Universality Class ◽  
Transition To Turbulence ◽  
Free Boundaries ◽  
Turbulent Structures ◽  
Continuous Transition ◽  
Normal Representation ◽  
Onset Of Turbulence ◽  
Planar Shear ◽  
Order Of Magnitude

We examine the onset of turbulence in Waleffe flow – the planar shear flow between stress-free boundaries driven by a sinusoidal body force. By truncating the wall-normal representation to four modes, we are able to simulate system sizes an order of magnitude larger than any previously simulated, and thereby to attack the question of universality for a planar shear flow. We demonstrate that the equilibrium turbulence fraction increases continuously from zero above a critical Reynolds number and that statistics of the turbulent structures exhibit the power-law scalings of the (2 + 1)-D directed-percolation universality class.

Transition to turbulence in a shear flow

1999 ◽  
Vol 60 (1) ◽  
pp. 509-517 ◽  
Author(s):  
Bruno Eckhardt ◽  
Alois Mersmann
Keyword(s):  
Shear Flow ◽  
Transition To Turbulence

scholarly journals Vortex-induced vibrations of a long flexible cylinder in shear flow

2011 ◽  
Vol 677 ◽  
pp. 342-382 ◽  
Author(s):  
REMI BOURGUET ◽  
GEORGE E. KARNIADAKIS ◽  
MICHAEL S. TRIANTAFYLLOU
Keyword(s):  
Shear Flow ◽  
Vortex Shedding ◽  
Cross Flow ◽  
Maximum Velocity ◽  
Travelling Wave ◽  
Transition To Turbulence ◽  
Wave Component ◽  
Flexible Cylinder ◽  
Vortex Induced Vibrations ◽  
Lock In

We investigate the in-line and cross-flow vortex-induced vibrations of a long cylindrical tensioned beam, with length to diameter ratio L/D = 200, placed within a linearly sheared oncoming flow, using three-dimensional direct numerical simulation. The study is conducted at three Reynolds numbers, from 110 to 1100 based on maximum velocity, so as to include the transition to turbulence in the wake. The selected tension and bending stiffness lead to high-wavenumber vibrations, similar to those encountered in long ocean structures. The resulting vortex-induced vibrations consist of a mixture of standing and travelling wave patterns in both the in-line and cross-flow directions; the travelling wave component is preferentially oriented from high to low velocity regions. The in-line and cross-flow vibrations have a frequency ratio approximately equal to 2. Lock-in, the phenomenon of self-excited vibrations accompanied by synchronization between the vortex shedding and cross-flow vibration frequencies, occurs in the high-velocity region, extending across 30% or more of the beam length. The occurrence of lock-in disrupts the spanwise regularity of the cellular patterns observed in the wake of stationary cylinders in shear flow. The wake exhibits an oblique vortex shedding pattern, inclined in the direction of the travelling wave component of the cylinder vibrations. Vortex splittings occur between spanwise cells of constant vortex shedding frequency. The flow excites the cylinder under the lock-in condition with a preferential in-line versus cross-flow motion phase difference corresponding to counter-clockwise, figure-eight orbits; but it damps cylinder vibrations in the non-lock-in region. Both mono-frequency and multi-frequency responses may be excited. In the case of multi-frequency response and within the lock-in region, the wake can lock in to different frequencies at various spanwise locations; however, lock-in is a locally mono-frequency event, and hence the flow supplies energy to the structure mainly at the local lock-in frequency.

A new roll-type instability in an oscillating fluid plane

1994 ◽  
Vol 268 ◽  
pp. 293-313 ◽  
Author(s):  
Edward W. Bolton ◽  
J. Maurer
Keyword(s):  
Shear Flow ◽  
Stokes Equation ◽  
Maximum Amplitude ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Secondary Wave ◽  
Initial Increase ◽  
Parallel Plates ◽  
Navier Stokes Equation ◽  
Roll Type

A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).

An Energy-Based Similarity Subgrid-Scale Model in Two-Dimensional Planar Shear Flow

2013 ◽  
Vol 694-697 ◽  
pp. 594-600
Author(s):  
Yu Xuan Zhang ◽  
Song Ping Wu
Keyword(s):  
Shear Flow ◽  
Scale Model ◽  
Two Dimensional ◽  
Subgrid Scale ◽  
Planar Shear ◽  
New Type ◽  
Subgrid Scale Model ◽  
Layer Flow ◽  
Refined Grid ◽  
Dissipative Scale

A new type of similarity subgrid-scale (SGS) model which based on energy and dissipative scale isotropy assumption is presented. This model combines the advantages of traditional Smagorinsky SGS model with similarity SGS model. And a two-dimensional shear layer flow is simulated using refined grid result as a standard and comparing witch LES method including multiple SGS models. The results indicate that the result of SIM model much approximates to refined grid result than other SGS models.

On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

1973 ◽  
Vol 59 (2) ◽  
pp. 281-335 ◽  
Author(s):  
I. J. Wygnanski ◽  
F. H. Champagne
Keyword(s):  
Energy Balance ◽  
Turbulent Flows ◽  
Turbulent Energy ◽  
Turbulent Pipe Flow ◽  
Entire Cross Section ◽  
Turbulent Fluid ◽  
Dissipation Term ◽  
Onset Of Turbulence ◽  
Order Of Magnitude ◽  
Pressure Transport

Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally atRe> 5 × 104. Transition could be initiated at lowerReby introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.Mixed laminar and turbulent flows were observed far downstream for\[ 2000 < Re < 2700 \]when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lowerRe. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.

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