Applications of Conformal Mapping to Complex Velocity Potential of the Flow of an Ideal Fluid

2017 ◽  
Vol 52 (3) ◽  
pp. 196-202
Author(s):  
Mohammed Mukhtar Mohammed Zabih ◽  
R.M.Lahu rikar
Keyword(s):  
Conformal Mapping ◽  
Ideal Fluid ◽  
Velocity Potential ◽  
Complex Velocity ◽  
Complex Velocity Potential

scholarly journals The Two-Phase Hell-Shaw Flow: Construction of an Exact Solution

2013 ◽  
Vol 18 (1) ◽  
pp. 249-257
Author(s):  
K.R. Malaikah
Keyword(s):  
Exact Solution ◽  
Velocity Potential ◽  
Time Dependent ◽  
Computational Domain ◽  
Phase Problem ◽  
Complex Velocity ◽  
Two Phase ◽  
Interface Evolution ◽  
Complex Velocity Potential ◽  
Branch Cuts

We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem

The almost-highest wave: a simple approximation

1979 ◽  
Vol 94 (2) ◽  
pp. 269-273 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Free Surface ◽  
Gravity Wave ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Simple Approximation ◽  
Complex Velocity ◽  
Complex Velocity Potential

The crest of a steep, symmetric gravity wave is shown to be closely approximated by the expression \[ x+iy = \frac{\alpha +\gamma i\chi}{(\beta + i\chi)^{\frac{1}{3}}}, \] where x, y are co-ordinates in the vertical plane, χ is the complex velocity potential and α, β, γ are certain constants. This expression is asymptotically correct both for small and for large values of |χ|; and the free surface agrees with the exact profile calculated by Longuet-Higgins & Fox (1977) everywhere to within 1·5 per cent. The pressure at the surface is constant to within 5 per cent.

The solitary wave of maximum amplitude

1966 ◽  
Vol 26 (2) ◽  
pp. 309-320 ◽  
Author(s):  
Charles W. Lenau
Keyword(s):  
Power Series ◽  
Solitary Wave ◽  
Velocity Potential ◽  
Maximum Amplitude ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Complex Velocity ◽  
Constant Form ◽  
Complex Velocity Potential ◽  
Infinite Power

The maximum amplitude of the solitary wave of constant form is determined to be 0·83b, where b is the depth far from the crest. In the analysis it is assumed that the crest is pointed and the motion is two-dimensional and irrotational. The complex velocity potential is expressed in terms of known singularities and an infinite power series with unknown coefficients. Approximate solutions are obtained by truncating the power series after N terms, where N = 1, 3, 5, 7, and 9. The amplitude, a measure of the error, and several other pertinent quantities are computed for each value of N.

The Disturbance Due to a Slender Ship Oscillating in Waves in a Fluid of Finite Depth

1966 ◽  
Vol 10 (04) ◽  
pp. 242-252 ◽  
Author(s):  
V. J. Monacella
Keyword(s):  
Ideal Fluid ◽  
Asymptotic Approximation ◽  
Velocity Potential ◽  
Wave Length ◽  
Hydrodynamic Pressure ◽  
Finite Depth ◽  
First Order ◽  
Incident Plane ◽  
Progressive Waves ◽  
Body Potential

The disturbance due to a ship, free to oscillate on the surface of an ideal fluid of finite depth, is studied. The ship is in the presence of oblique, incident, plane progressive waves. Green's theorem is used to represent the velocity potential, and an asymptotic approximation for the first-order slender-body potential valid for all points in the fluid to within a wave length of the ship is found. This is used to determine the hydrodynamic pressure on the bottom of the fluid. Numerical results are presented for the case of a spheroid.

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