XXXIII.—Applications of Elliptic Functions to Wind Tunnel Interference

SummaryA general formula is obtained for the interference velocity when an aerofoil with elliptically distributed circulation is in a closed or open wind tunnel of any cross-section. The mapping of the section on the interior of a circle is given in terms of the Jacobian elliptic functions appropriate to the ellipse and rectangle. The result is worked out for an aerofoil which spans the focal distance in a tunnel whose section is an ellipse.

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Jacobian Elliptic Functions

Foundations of Space Dynamics ◽

10.1002/9781119455301.app2 ◽

2021 ◽

pp. 345-346

Keyword(s):

Elliptic Functions ◽

Jacobian Elliptic Functions

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Jacobian elliptic functions and a family of bivariate peak polynomials

European Journal of Combinatorics ◽

10.1016/j.ejc.2021.103371 ◽

2021 ◽

Vol 97 ◽

pp. 103371

Author(s):

Shi-Mei Ma ◽

Jun Ma ◽

Yeong-Nan Yeh ◽

Roberta R. Zhou

Keyword(s):

Elliptic Functions ◽

Jacobian Elliptic Functions

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Influence of the Side Walls on the Turbulent Center-Plane Boundary-Layer in a Square Duct

Journal of Fluids Engineering ◽

10.1115/1.3448621 ◽

1978 ◽

Vol 100 (1) ◽

pp. 91-96 ◽

Cited By ~ 38

Author(s):

V. de Brederode ◽

P. Bradshaw

Keyword(s):

Boundary Layer ◽

Wind Tunnel ◽

Flat Plate ◽

Cross Section ◽

Secondary Flows ◽

Plane Boundary ◽

Square Duct ◽

Streamwise Pressure Gradient ◽

Side Walls ◽

Working Section

Measurements in the entry region of a square duct (specifically, a wind-tunnel working section) show that the direct effect of stress-induced secondary flows in the corners on the center-plane boundary layer is negligible for boundary layers thinner than about one-fourth of the duct width. Further, the effects of streamwise pressure gradient and of quasi-collinear lateral convergence tend to cancel so that the velocity profiles and skin friction are quite close to those on a flat plate. This shows that the boundary layer on the floor of a wind tunnel of constant, square cross section can be used to simulate a flat-plate flow even when the boundary layer thickness is as large as one-fourth of the tunnel height.

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ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD

Modern Physics Letters B ◽

10.1142/s0217984910022846 ◽

2010 ◽

Vol 24 (08) ◽

pp. 761-773

Author(s):

HONG ZHAO

Keyword(s):

Difference Equations ◽

Elliptic Function ◽

Analytical Study ◽

Elliptic Functions ◽

Expansion Method ◽

Periodic Wave ◽

Jacobian Elliptic Function ◽

Jacobian Elliptic Functions ◽

Periodic Wave Solutions ◽

Trigonometric Function Solutions

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

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