Small perturbations of plane unsteady motion of an ideal incompressible fluid with a free boundary in the shape of an ellipse

1974 ◽  
Vol 12 (4) ◽  
pp. 530-538
Author(s):  
V. V. Pukhnachev
Keyword(s):  
Free Boundary ◽  
Incompressible Fluid ◽  
Ideal Incompressible Fluid ◽  
Unsteady Motion ◽  
Small Perturbations

Conformal mapping, Padé approximants, and an example of flow with a significant deformation of the free boundary

2014 ◽  
Vol 25 (6) ◽  
pp. 729-747 ◽  
Author(s):  
E. A. KARABUT ◽  
A. A. KUZHUGET
Keyword(s):  
Velocity Field ◽  
Free Boundary ◽  
Power Series ◽  
Conformal Mapping ◽  
Incompressible Fluid ◽  
Padé Approximants ◽  
Ideal Incompressible Fluid ◽  
Inertial Motion ◽  
Pade Approximants ◽  
Summation Of Series

A problem of plane inertial motion of an ideal incompressible fluid with a free boundary, which initially has a quadratic velocity field, is studied by semi-analytical methods. A conformal mapping of the domain occupied by the fluid onto a unit circle is sought in the form of a power series with respect to time. Summation of series is performed by using Padé approximants.

Unsteady flows with a zero acceleration on the free boundary

2014 ◽  
Vol 754 ◽  
pp. 308-331 ◽  
Author(s):  
E. A. Karabut ◽  
E. N. Zhuravleva
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Unsteady Flows ◽  
Ideal Incompressible Fluid ◽  
Hopf Equation ◽  
New Approach

AbstractA new approach to the construction of exact solutions of unsteady equations for plane flows of an ideal incompressible fluid with a free boundary is proposed. It is demonstrated that the problem is significantly simplified and reduces to solving the Hopf equation if the acceleration on the free surface is equal to zero. Some examples of exact solutions are given.

scholarly journals Weak Dual Pairs and Jetlet Methods for Ideal Incompressible Fluid Models in $$n \ge 2$$ n ≥ 2 Dimensions

2016 ◽  
Vol 26 (6) ◽  
pp. 1723-1765 ◽  
Author(s):  
C. J. Cotter ◽  
J. Eldering ◽  
D. D. Holm ◽  
H. O. Jacobs ◽  
D. M. Meier
Keyword(s):  
Incompressible Fluid ◽  
Ideal Incompressible Fluid ◽  
Fluid Models ◽  
Dual Pairs
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