Boundary Layers on Characteristic Surfaces for Time-Dependent Rotating Flows

1983 ◽  
Vol 50 (2) ◽  
pp. 251-254 ◽  
Author(s):  
R. F. Gans
Keyword(s):  
Boundary Layers ◽  
Kinematic Viscosity ◽  
Normal Component ◽  
Rotating Flows ◽  
Rotation Vector ◽  
Time Dependent ◽  
Normal Vector ◽  
Length Scale ◽  
Rotation Vectors ◽  
Typical Length

Time-dependent motion of a fluid in a container rotating at Ω is characterized by boundary layers on the container surfaces if ν/Ω, where ν denotes kinematic viscosity, is small compared to the square of a typical length of the container. Let the frequency of the motion, measured in a corotating coordinate system, be ωΩ. If ω ~ 1, then the length scale of the boundary layer is (ν/Ω)1/2, unless |ω| is equal to twice the normal component of the unit rotation vector. If |ω| does equal twice the normal component of the unit rotation vector, scales of (ν/ΩL2)1/3 L and (ν/ΩL2)1/4 L are possible. If the normal vector and rotation vectors are parallel, the former scale vanishes.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

ROTATION VECTORS FOR TORAL MAPS AND FLOWS: A TUTORIAL

1995 ◽  
Vol 05 (02) ◽  
pp. 321-348 ◽  
Author(s):  
JAMES A. WALSH
Keyword(s):  
Dynamical Systems ◽  
Rotation Number ◽  
Chaotic Behavior ◽  
Invariant Tori ◽  
Mode Locking ◽  
Rotation Vector ◽  
Higher Genus ◽  
Rotation Vectors ◽  
Dissipative Dynamical Systems ◽  
Rotation Set

This paper is an introduction to the concept of rotation vector defined for maps and flows on the m-torus. The rotation vector plays an important role in understanding mode locking and chaos in dissipative dynamical systems, and in understanding the transition from quasiperiodic motion on attracting invariant tori in phase space to chaotic behavior on strange attractors. Throughout this article the connection between the rotation vector and the dynamics of the map or flow is emphasized. We begin with a brief introduction to the dimension one setting, in which case the rotation vector reduces to the well known rotation number of H. Poincaré. A survey of the main results concerning the rotation number and bifurcations of circle maps is presented. The various definitions of rotation vector in the higher dimensional setting are then introduced with emphasis again placed on how certain properties of the rotation set relate to the dynamics of the map or flow. The dramatic differences between results in dimension two and results in higher dimensions are also presented. The tutorial concludes with a brief introduction to extensions of the concept of rotation vector to the setting of dynamical systems defined on surfaces of higher genus.

Modification of the turbulent length scale by wall permeability in rough-wall boundary layers

2020 ◽  
Vol 2020.95 (0) ◽  
pp. 07_713
Author(s):  
Yuki OKAZAKI ◽  
Yumeto TAKASE ◽  
Ayumi SHIMIZU ◽  
Yusuke KUWATA ◽  
Kazuhiko SUGA
Keyword(s):  
Boundary Layers ◽  
Rough Wall ◽  
Length Scale ◽  
Turbulent Length Scale ◽  
Wall Boundary ◽  
Wall Permeability

Boundary Layers in Rotating Flows.

1964 ◽  
Author(s):  
Nicholas Rott ◽  
W. S. Lewellen
Keyword(s):  
Boundary Layers ◽  
Rotating Flows

Investigation of a Method for the General Analysis of Time Dependent Two-Dimensional Laminar Boundary Layers

1968 ◽  
Vol 90 (4) ◽  
pp. 563-570 ◽  
Author(s):  
S. J. Koob ◽  
D. E. Abbott
Keyword(s):  
Boundary Layers ◽  
Transient Flow ◽  
Order Approximation ◽  
Method Of Lines ◽  
Skin Friction Coefficient ◽  
Time Dependent ◽  
Two Dimensional ◽  
Weighted Residuals ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers

A method is given for the analysis of time dependent two-dimensional incompressible laminar boundary layers. The technique is a combination of the method of weighted residuals and the method of lines, and reduces the boundary-layer equations to an Nth order approximation in terms of a system of ordinary differential equations. The method is demonstrated by solving the transient flow over a semi-infinite flat plate and the results are compared with known asymptotic solutions. For a third approximation, the steady-state skin friction coefficient given by the present method agrees with the Blasius solution within 0.1 percent.

Uniform momentum zones in turbulent boundary layers

2015 ◽  
Vol 786 ◽  
pp. 309-331 ◽  
Author(s):  
Charitha M. de Silva ◽  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Linear Increase ◽  
Length Scale ◽  
Image Velocimetry ◽  
Order Of Magnitude ◽  
Log Linear

Structural properties of regions of uniform streamwise momentum in turbulent boundary layers are examined using experimental databases obtained from particle image velocimetry. This investigation employs a large range of Reynolds numbers, spanning more than an order of magnitude ($Re_{{\it\tau}}=10^{3}{-}10^{4}$), enabling us to provide a detailed description of uniform momentum zones as a function of Reynolds number. Our analysis starts by examining the identification criterion used by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54) to report the presence of uniform momentum zones in turbulent boundary layers. This criterion is then applied to show that a zonal-like structural arrangement is prevalent in all datasets examined, emphasising its importance in the structural organisation. Streamwise velocity fluctuations within the zones are observed to be small but they are bounded by distinct step changes in streamwise momentum which indicate that shear layers of intense vorticity separate each zone. A log-linear increase in the number of these zones with increasing Reynolds number is revealed, together with an increase in the thicknesses of zones with increasing distance from the wall. These results support a hierarchical length-scale distribution of coherent structures, which generate zonal-like organisation within turbulent boundary layers. Interpretation of these findings is aided by employing synthetic velocity fields generated using a model based on the attached eddy hypothesis, which is described in the work of Perry and co-workers. Comparisons between the model and experimental results show that a hierarchy of self-similar structures leads to population densities and length-scale distributions of uniform momentum zones that closely adhere to those observed experimentally in this study.

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