Shear flows of non-linear visco-elastic fluids

Geometrically non-linear problem of orthotropic thin rectangular panel post-buckling behavior with shear is solved. Deflection function takes all-boundary rigid support conditions into account. Based on derived solution method of smooth panels design which can be used for aircraft structures rib and spar webs optimal parameters is suggested.

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A non-linear k-epsilon model for turbulent shear flows

10.2514/6.1998-3983 ◽

1998 ◽

Cited By ~ 8

Author(s):

Tsan-Hsing Shih ◽

Nan-Suey Liu ◽

Kuo-Huey Chen

Keyword(s):

Shear Flows ◽

Turbulent Shear ◽

Non Linear ◽

Turbulent Shear Flows

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A non-linear theory of turbulence onset in a shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112067001144 ◽

1967 ◽

Vol 29 (4) ◽

pp. 721-729 ◽

Cited By ~ 6

Author(s):

E. M. Hasen

Keyword(s):

Large Scale ◽

Shear Flows ◽

Incompressible Flows ◽

Linear Equations ◽

Finite Amplitude ◽

Small Scale ◽

Two Dimensional ◽

Initial Amplitude ◽

Mean Velocity ◽

Non Linear

Turbulence onset is considered in viscous incompressible flows. Development of fluctuations in an infinite flow with a constant gradient of mean velocity ∂U1/∂x2 = const., U2 = U3 = 0 is rigorously treated.It is shown that two-dimensional eddy fluctuations, with infinitesimal initial amplitude A and scale of initial eddies l, increase in this flow so that the maximum ratio max ε(t)/ε(0) of their energy at the moment t to the initial energy exceeds any prescribed value as the Reynolds number R = (∂U1/∂x2) l2/v increases. The analysis of the non-linear equations obtained in the paper which describe development of fluctuations with a finite amplitude leads to the conclusion that there exists a’ stability barrier’ Ã (R) for the initial amplitude of eddy fluctuations. If A < Ã (R), then fluctuations decay as t → ∞, and if A > Ã(R) the energy of fluctuations does not decay. As R → ∞, Ã(R) → 0 according to the inequalities \[ l(\partial U_1/\partial x_2)K_2/R^{\frac{2}{3}}\leqslant \tilde{A}(R)\leqslant l(\partial U_1/\partial x_2)\,K_1/R^{\frac{2}{3}}. \] It is shown that the non-linear mechanism of preventing turbulence from decay involves generation of large-scale turbulent oscillations which then transmit energy to small-scale motions.The described mechanism of turbulence onset from small eddies in shear flows appears to be of universal character. It is interesting that several qualitative characteristics of turbulence observed in various shear flows can be rigorously deduced even in a model where disturbances remain two-dimensional.

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B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

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