Momentum Integral for Curved Shear Layers

1975 ◽  
Vol 97 (2) ◽  
pp. 253-256 ◽  
Author(s):  
Ronald M. C. So
Keyword(s):  
Boundary Layer ◽  
Shear Layers ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Displacement Effect ◽  
Curved Boundary ◽  
Curvature Effects ◽  
Von Karman ◽  
Momentum Integral ◽  
Von Kármán

If the exact metric influence of curvature is retained and the displacement effect neglected, it can be shown that the momentum integral for two-dimensional, curved boundary-layer flows is identical to the von Karman momentum integral. As a result, attempts by previous researchers to account for longitudinal curvature effects by adding more terms to the momentum integral are shown to be correct.

Absolute instability of the von Kármán, Bödewadt and Ekman flows between a rotating disc and a stationary lid

2005 ◽  
Vol 363 (1830) ◽  
pp. 1131-1144 ◽  
Author(s):  
Hosne Ara Jasmine ◽  
Jitesh S.B Gajjar
Keyword(s):  
Boundary Layer ◽  
Incompressible Fluid ◽  
Spectral Method ◽  
Convective Instability ◽  
Absolute Instability ◽  
Boundary Layer Flows ◽  
Rotating Disc ◽  
Von Karman ◽  
The Stability ◽  
Von Kármán

The stability of a family of boundary-layer flows, which includes the von Kármán, Bödewadt and Ekman flows for a rotating incompressible fluid between a rotating disc and a stationary lid, is investigated. Numerical computations with the use of a spectral method are carried out to analyse absolute and convective instability. It is shown that the stability of the system is enhanced with a decrease in distance between the disc and the lid.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

Hydrodynamics and behaviour of Simuliidae larvae (Diptera)

1986 ◽  
Vol 64 (6) ◽  
pp. 1295-1309 ◽  
Author(s):  
M. M. Chance ◽  
D. A. Craig
Keyword(s):  
Boundary Layer ◽  
Lower Boundary ◽  
The Body ◽  
The Other ◽  
Avoidance Reaction ◽  
Larval Body ◽  
Video Recordings ◽  
Von Karman ◽  
Von Kármán ◽  
Lower Boundary Layer

Detailed water flow around larvae of Simulium vittatum Zett. (sibling IS-7) was investigated using flow tanks, aluminium flakes, pigment, still photography, cinematography, and video recordings. Angle of deflection of a larva from the vertical has a hyperbolic relationship to water velocity. Velocity profiles around larvae show that the body is in the boundary layer. Frontal area of the body decreases as velocity increases. Disturbed larvae exhibit "avoidance reaction" and pull the body into the lower boundary layer. Longitudinal twisting and yawing of the larval body places one labral fan closer to the substrate, the other near the top of the boundary layer. Models and live larvae were used to demonstrate the basic hydrodynamic phenomenon of downstream paired vortices. Body shape and feeding stance result in one of the vortices remaining in the lower boundary layer. The other rises up the downstream side of the body, passes through the lower fan, then forms a von Karman trail of detaching vortices. This vortex entrains particulate matter from the substrate, which larvae then filter. Discharge of water into this upper vortex remains constant at various velocities and only water between the substrate and top of the posterior abdomen is incorporated into it. The upper fan filters water only from the top of the boundary layer. Formation of vortices probably influences larval microdistribution and filter feeding. Larvae positioned side by side across the flow mutually influence flow between them, thus enhancing feeding. Larvae downstream of one another may use information from the von Karman trail of vortices to position themselves advantageously.

The Isobars in Boundary Layers at Supersonic Speeds

1968 ◽  
Vol 19 (2) ◽  
pp. 105-126 ◽  
Author(s):  
D. F. Myring ◽  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Equations Of Motion ◽  
Normal Pressure ◽  
Simple Extension ◽  
Pressure Gradients ◽  
Boundary Layer Flows ◽  
Hyperbolic Flow ◽  
The Individual ◽  
Momentum Integral

SummaryFor boundary layer flows over curved surfaces at moderately high supersonic speeds the existence of normal pressure gradients within the boundary layer becomes important even for small curvatures and they cannot be ignored. The describing equations are basically parabolic in form so that the simplifications inherent in hyperbolic flows would not at first sight seem to be relevant. However, the equations of motion for a two-dimensional, supersonic, rotational, viscous flow are analysed along the lines of a hyperbolic flow and the individual effects of viscosity and vorticity are examined with regard to the isobar distributions. It is found that these two properties have compensating effects and the experimental evidence presented confirms the conclusion that inside the boundary layer the isobars follow much the same rules as those which determine the isobars in the external hyperbolic flow. Since for turbulent boundary layers the fullness of the Mach number profile produces almost linear Mach lines in the boundary layer, this provides a simple extension to the methods of analysis, and the momentum integral equation is reformulated using a swept element bounded by linear isobars. The final equation is similar in form to the conventional one except that the momentum and displacement thicknesses are now defined by integrals along the swept isobars, and all normal pressure gradients due to centrifugal effects are accounted for.

scholarly journals A New Value of the von Kármán Constant: Implications and Implementation

2009 ◽  
Vol 48 (5) ◽  
pp. 923-944 ◽  
Author(s):  
Edgar L. Andreas
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Transfer Coefficients ◽  
Obukhov Length ◽  
Von Karman ◽  
Roughness Lengths ◽  
Experimental Values ◽  
Definition Of ◽  
Von Kármán

Abstract The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD), the transfer coefficients for sensible (CH) and latent (CE) heat, and the roughness lengths for wind speed (z0), temperature (zT), and humidity (zQ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD, CH, CE, z0, zT, and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

Instabilities of the von Kármán Boundary Layer

2015 ◽  
Vol 67 (3) ◽  
Author(s):  
R. J. Lingwood ◽  
P. Henrik Alfredsson
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Direct Numerical Simulations ◽  
Layer Model ◽  
Complex Flow ◽  
Von Karman ◽  
Dimensional Boundary ◽  
Flow Configurations ◽  
Von Kármán

Research on the von Kármán boundary layer extends back almost 100 years but remains a topic of active study, which continues to reveal new results; it is only now that fully nonlinear direct numerical simulations (DNS) have been conducted of the flow to compare with theoretical and experimental results. The von Kármán boundary layer, or rotating-disk boundary layer, provides, in some senses, a simple three-dimensional boundary-layer model with which to compare other more complex flow configurations but we will show that in fact the rotating-disk boundary layer itself exhibits a wealth of complex instability behaviors that are not yet fully understood.

Comparison of Turbulent Boundary Layer Profiles Modified With Injection or Uniform Concentration of Drag-Reducing Polymer Solution

2020 ◽  
Author(s):  
Brian R. Elbing
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Polymer Concentration ◽  
Weissenberg Number ◽  
Polymer Injection ◽  
Von Karman ◽  
Polymer Properties ◽  
Polymer Drag Reduction ◽  
Von Kármán

Abstract The current study explores the influence of polymer drag reduction on the near-wall velocity distribution in a turbulent boundary layer. The classical view is that the polymers modify the intercept constant within the log-region without impacting the von Kármán coefficient, which results in the log-region being unaltered though shifted outward from the wall. However, it has been recently shown that this is not accurate, especially at high drag reduction (> 40%). Past work examining the von Kármán coefficient and intercept constant has shown that polymer properties must impact the deviations, but without any quantification of the dependence. This work reviews the literature to make estimates of the local polymer properties and then demonstrates that the scatter at HDR can be attributed to variations in the Weissenberg number. In addition, new polymer ocean results are incorporated and shown to be quite consistent with polymer injection results using the maximum polymer concentration to define the polymer properties.

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