scholarly journals Some Nonlinear Vortex Solutions

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Michael C. Haslam ◽  
Christopher J. Smith ◽  
Ghada Alobaidi ◽  
Roland Mallier
Keyword(s):  
Steady State ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
Specific Form ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Vortex Solutions

We consider the steady-state two-dimensional motion of an inviscid incompressible fluid which obeys a nonlinear Poisson equation. By seeking solutions of a specific form, we arrive at some interesting new nonlinear vortex solutions.

The aerodynamic forces on an oscillating aerofoil in a free jet

1955 ◽  
Vol 229 (1177) ◽  
pp. 235-250 ◽  
Keyword(s):  
Wind Tunnel ◽  
Incompressible Fluid ◽  
Classical Theory ◽  
Direct Application ◽  
Two Dimensional ◽  
Aerodynamic Forces ◽  
Small Oscillations ◽  
Free Jet ◽  
Inviscid Incompressible Fluid ◽  
Wind Tunnel Measurements

The forces acting on an aerofoil placed centrally in a two-dimensional jet of inviscid incompressible fluid are calculated exactly for the case when the aerofoil is performing small oscillations about its mean position. The theory is a generalization of the classical theory due to Theodorsen and others for an oscillating aerofoil in an infinite stream. The results, which are expressed in terms of a ‘generalized Theodorsen function’, have a direct application to the correction of open-jet wind-tunnel measurements on oscillating aerofoils.

scholarly journals Stability and instability results for the 2D [alpha]-Euler equations

2017 ◽  
Author(s):  
◽  
Shibi Kapisthalam Vasudevan
Keyword(s):  
Steady State ◽  
Euler Equations ◽  
Nonlinear Term ◽  
Zero Mode ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Fourier Decomposition ◽  
Inviscid Incompressible Fluid ◽  
Stability And Instability ◽  
Steady State Solutions

We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u [times] [del.])u in the classical Euler equations of inviscid incompressible fluid by the term (v [times] [del.])u, where v is the regularized velocity satisfying (1 -[alpha]2[delta])v [equals] u, and [alpha] [greater than] 0. In the first part of the thesis, for the a-model, we develop analogues of the classical Arnol'd type stability criteria based on the energy-Casimir method for several settings including multi connected domains, periodic channels, and others. In the second part of the thesis, we study stability of a particular steady state, the unidirectional solution of the a-Euler equation on the two dimensional torus, having only one non zero mode in its Fourier decomposition. Using continued fractions, we give a proof of instability of the steady state under fairly general conditions. In the third part of the thesis we study various properties of a family of elliptic operators introduced by Zhiwu Lin in his work on instability of steady state solutions of the two dimensional Euler equations. This involves Birman-Schwinger type operators associated with the linearization of the Euler equations about the steady state and certain perturbation determinants.

The distortion of a bubble in a corner flow

2000 ◽  
Vol 11 (2) ◽  
pp. 171-179 ◽  
Author(s):  
E. OZUGURLU ◽  
J.-M. VANDEN-BROECK
Keyword(s):  
Incompressible Fluid ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Corner Flow

The distortion of a two-dimensional bubble (or drop) in a corner flow of an inviscid incompressible fluid is considered. Numerical solutions are obtained by series truncation. The results confirm and extend previous calculations.

scholarly journals Two-dimensional jet aimed vertically upwards

1993 ◽  
Vol 34 (4) ◽  
pp. 393-400 ◽  
Author(s):  
Jean-Marc Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Finite Differences ◽  
Two Dimensional ◽  
Free Surfaces ◽  
Inviscid Incompressible Fluid ◽  
Surface Profiles

AbstractA steady two-dimensional jet of an inviscid incompressible fluid rising and falling under gravity is considered. The jet is aimed vertically upwards and the flow is assumed to be bounded entirely by two free surfaces. The problem is solved numerically by finite differences. Accurate results for the free surface profiles are presented.

The formation of vortex streets

1962 ◽  
Vol 13 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Frederick H. Abernathy ◽  
Richard E. Kronauer
Keyword(s):  
Incompressible Fluid ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Vortex Sheets ◽  
Linear Interaction ◽  
Inviscid Incompressible Fluid ◽  
Fixed Distance ◽  
Vortex Streets ◽  
Non Linear

The formation of vortex streets in the wake of two-dimensional bluff bodies can be explained by considering the non-linear interaction of two infinite vortex sheets, initially a fixed distance, h, apart, in an inviscid incompressible fluid. The interaction of such sheets (represented in the calculation by rows of point-vortices) is examined in detail for various ratios of h to the wavelength, a, of the initial disturbance. The number and strength of the concentrated regions of vorticity formed in the interaction depend very strongly on h/a. The non-linear interaction of the two vortex sheets explains both the cancellation of vorticity and vortex-street broadening observed in the wakes of bluff bodies.

scholarly journals Structure of a linear array of hollow vortices of finite cross-section

1976 ◽  
Vol 74 (3) ◽  
pp. 469-476 ◽  
Author(s):  
G. R. Baker ◽  
P. G. Saffman ◽  
J. S. Sheffield
Keyword(s):  
Incompressible Fluid ◽  
Cross Section ◽  
Linear Array ◽  
Critical Value ◽  
Steady Solution ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
The Stability

Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A½/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

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