scholarly journals Algebraic Growth and Streak Formation in Shear Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S218-S218
Author(s):  
Marten T. Landahl
Keyword(s):  
Shear Flow ◽  
Velocity Component ◽  
High Speed ◽  
Shear Flows ◽  
Three Dimensional ◽  
Shear Layers ◽  
Turbulent Shear ◽  
Algebraic Instability ◽  
Horizontal Pressure ◽  
The Difference

By examination of the long-term behavior of an initial three-dimensional and localized disturbance in an inflection-free shear flow a detailed study of the algebraic instability mechanism of an inviscid shear flow (Landahl, 1980) is carried out. It is shown that the vertical velocity component will tend to zero at least as fast as 1/t whereas, as a result of a nonzero liftup of the fluid elements, the streamwise disturbence velocity component will tend to a limiting finite value in a convected frame of reference. For an initial disturbence having a nonzero net vertical momentum along a streamline, the streamwise dimension of the disturbed region is found to grow indefinitely at a rate set by the difference between the maximum and minimum velocities in the parallel flow. The total kinetic energy of the disturbence therefore grows linearly in time through the formation of continuously elongating high-speed or low-speed regions. In these, internal shear layers are formed that intensify through the mechanism of spanwise stretching of the mean vorticity. The effect of a small viscosity is felt primarily in the shear layers so as to make them diffuse and eventually cause the disturbence to decay on a viscous time scale. For the streaky structures near a wall the horizontal pressure gradients are found to be small, making possible a simple approximate treatment of nonlinearty. Such an analysis suggests the possibility of the appearance of a rapid outflow event (“bursting”) from the wall that may occur at a finite time inversely proportional to the amplitude of the initial disturbance. On basis of the analysis presented it is proposed that algebraic growth is the primary mechanism for the formation of streaks in laminar and turbulent shear flows.

A note on an algebraic instability of inviscid parallel shear flows

1980 ◽  
Vol 98 (2) ◽  
pp. 243-251 ◽  
Author(s):  
M. T. Landahl
Keyword(s):  
Kinetic Energy ◽  
Wide Class ◽  
Shear Flows ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Constant Density ◽  
Disturbed Region ◽  
Streaky Structure ◽  
Algebraic Instability ◽  
Parallel Shear Flows

It is shown that all parallel inviscid shear flows of constant density are unstable to a wide class of initial infinitesimal three-dimensional disturbances in the sense that, according to linear theory, the kinetic energy of the disturbance will grow at least as fast as linearly in time. This can occur even when the disturbance velocities are bounded, because the streamwise length of the disturbed region grows linearly with time. This finding may have implications for the observed tendency of turbulent shear flows to develop a longitudinal streaky structure.

Numerical and Experimental Investigation of Secondary Flow in a High Speed Compressor Stator

1995 ◽  
Author(s):  
Y. Ohkita ◽  
H. Kodama ◽  
O. Nozaki ◽  
K. Kikuchi ◽  
A. Tamura
Keyword(s):  
Numerical Simulation ◽  
Experimental Investigation ◽  
Shear Flow ◽  
Secondary Flow ◽  
Total Pressure ◽  
High Speed ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Performance Recovery

A series of numerical and experimental studies have been conducted to understand the mechanism of loss generation in a high speed compressor stator with inlet radial shear flow over the span. In this study, numerical simulation is extensively used to investigate the complex three-dimensional flow in the cascades and to interpret the phenomena appeared in the high speed compressor tests. It has been shown that the inlet radial shear flow generated by upstream rotor had a significant influence on the stator secondary flow, and consequently on the total pressure loss. Redesign of the stator aiming at the reduction of loss by controlling secondary flow has been carried out and the resultant performance recovery was successfully demonstrated both numerically and experimentally.

Evaluation of fish-injury mechanisms during exposure to turbulent shear flow

2005 ◽  
Vol 62 (7) ◽  
pp. 1513-1522 ◽  
Author(s):  
Zhiqun Deng ◽  
Gregory R Guensch ◽  
Craig A McKinstry ◽  
Robert P Mueller ◽  
Dennis D Dauble ◽  
...  
Keyword(s):  
High Speed ◽  
Motion Tracking ◽  
Oncorhynchus Tshawytscha ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Control Group ◽  
Similar Data ◽  
Turbulent Shear Flow ◽  
Eye Injuries ◽  
Injury Mechanisms

Understanding the factors that injure or kill turbine-passed fish is important to the operation and design of the turbines. Motion-tracking analysis was performed on high-speed, high-resolution digital videos of juvenile salmonids exposed to a laboratory-generated shear environment to isolate injury mechanisms. Hatchery-reared fall chinook salmon (Oncorhynchus tshawytscha, 93–128 mm in length) were introduced into a submerged, 6.35-cm-diameter water jet at velocities ranging from 12.2 to 19.8 m·s–1, with a reference control group released at 3 m·s–1. Injuries typical of turbine-passed fish were observed and recorded. Three-dimensional trajectories were generated for four locations on each fish released. Time series of velocity, acceleration, force, jerk, and bending angle were computed from the three-dimensional trajectories. The onset of minor, major, and fatal injuries occurred at nozzle velocities of 12.2, 13.7, and 16.8 m·s–1, respectively. Opercle injuries occurred at 12.2 m·s–1 nozzle velocity, while eye injuries, bruising, and loss of equilibrium were common at velocities of 16.8 m·s–1 and above. Of the computed dynamic parameters, acceleration showed the strongest predictive power for eye and opercle injuries and overall injury level, and it may provide the best potential link between laboratory studies of fish injury, field studies designed to collect similar data in situ, and numerical modeling.

scholarly journals Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

2013 ◽  
Vol 731 ◽  
pp. 1-45 ◽  
Author(s):  
A. Riols ◽  
F. Rincon ◽  
C. Cossu ◽  
G. Lesur ◽  
P.-Y. Longaretti ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Shear Flows ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Global Bifurcations ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Systems Research ◽  
Hydrodynamic Shear

AbstractMagnetorotational dynamo action in Keplerian shear flow is a three-dimensional nonlinear magnetohydrodynamic process, the study of which is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics with transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles born out of saddle-node bifurcations. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to injection of both kinetic and magnetic energy for the problem of transition to turbulence and dynamo action in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to understand better the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.

On the Propagation of Sound in a High-Speed Non-Isothermal Shear Flow

2009 ◽  
Vol 8 (3) ◽  
pp. 199-230 ◽  
Author(s):  
L.M.B.C. Campos ◽  
M.H. Kobayashi
Keyword(s):  
Wave Equation ◽  
Shear Flow ◽  
Acoustic Wave ◽  
Sound Speed ◽  
High Speed ◽  
Shear Flows ◽  
Critical Layer ◽  
Acoustic Wave Equation ◽  
Mean Flow ◽  
Flow Vorticity

The propagation of sound in shear flows is relevant to the acoustics of wall and duct boundary layers, and to jet shear layers. The acoustic wave equation in a shear flow has been solved exactly only for a plane unidirectional homentropic mean shear flow, in the case of three velocity profiles: linear, exponential and hyperbolic tangent. The assumption of homentropic mean flow restricts application to isothermal shear flows. In the present paper the wave equation in an plane unidirectional shear flow with a linear velocity profile is solved in an isentropic non-homentropic case, which allows for the presence of transverse temperature gradients associated with the ***non-uniform sound speed. The sound speed profile is specified by the condition of constant enthalpy, i.e. homenergetic shear flow. In this case the acoustic wave equation has three singularities at finite distance (besides the point at infinity), viz. the critical layer where the Doppler shifted frequency vanishes, and the critical flow points where the sound speed vanishes. By matching pairs of solutions around the singular and regular points, the amplitude and phase of the acoustic pressure in calculated and plotted for several combinations of wavelength and wave frequency, mean flow vorticity and sound speed, demonstrating, among others, some cases of sound suppression at the critical layer.

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