On existence of two-dimensional nonstationary flows of an ideal incompressible liquid admitting a curl nonsummable to any power greater than 1

1992 ◽  
Vol 33 (5) ◽  
pp. 934-937 ◽  
Author(s):  
A. B. Morgulis
Keyword(s):  
Incompressible Liquid ◽  
Two Dimensional ◽  
Ideal Incompressible Liquid

Note on the Smith-Stone theory of fish propulsion

1964 ◽  
Vol 280 (1382) ◽  
pp. 398-408 ◽  
Keyword(s):  
Incompressible Liquid ◽  
Velocity Potential ◽  
Present Note ◽  
Flexible Plate ◽  
Two Dimensional ◽  
Ideal Incompressible Liquid ◽  
Wake Effect ◽  
Fish Propulsion ◽  
Perturbation Velocity ◽  
Two Dimensional Flow

The present note extends the theory of fish propulsion by E. H. Smith & D. E. Stone, taking into account the wake effect which was not discussed in the original paper. The motion of a fish is simulated by a flexible plate of infinitesimal thickness, infinite span, and constant chord length, moving in the two-dimensional flow field of an ideal incompressible liquid. The perturbation velocity potential for the flexible plate is obtained by solving the Laplace equation in an elliptic cylindrical co-ordinate system, while the wake velocity potential follows from the application of a method which is due to Theodorsen. The results are shown to be identical with those derived previously by Siekmann. A simple example is given for illustration and results predicted by theory are compared with experimental data.

Second-order Wagner theory for two-dimensional water-entry problems at small deadrise angles

2007 ◽  
Vol 572 ◽  
pp. 59-85 ◽  
Author(s):  
J. M. OLIVER
Keyword(s):  
Experimental Data ◽  
Asymptotic Analysis ◽  
Incompressible Liquid ◽  
Water Entry ◽  
Second Order ◽  
Two Dimensional ◽  
Predictive Capability ◽  
Wagner’S Theory ◽  
Wagner Theory ◽  
Matched Asymptotic Analysis

The theory of Wagner from 1932 for the normal symmetric impact of a two-dimensional body of small deadrise angle on a half-space of ideal and incompressible liquid is extended to derive the second-order corrections for the locations of the higher-pressure jet-root regions and for the upward force on the impactor using a systematic matched-asymptotic analysis. The second-order predictions for the upward force on an entering wedge and parabola are compared with numerical and experimental data, respectively, and it is concluded that a significant improvement in the predictive capability of Wagner's theory is afforded by proceeding to second order.

Note on the motion of viscous liquid past a parabolic cylinder

1954 ◽  
Vol 50 (1) ◽  
pp. 125-130 ◽  
Author(s):  
W. R. Dean
Keyword(s):  
Viscous Liquid ◽  
Stream Function ◽  
Incompressible Liquid ◽  
Parabolic Cylinder ◽  
Viscous Incompressible Liquid ◽  
Two Dimensional ◽  
Approximate Expressions

1. In §§ 2–4 of this paper approximate expressions are found for the stream function and pressure in the steady two-dimensional motion of viscous incompressible liquid past a fixed parabolic cylinder; exact expressions for the stream-function and pressure in a perfect liquid are derived as limits in § 5.

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