Motion of an Interface between Two Uniform-Vorticity Regions in Two-Dimensional Inviscid Fluids

1989 ◽  
Vol 58 (1) ◽  
pp. 121-128
Author(s):  
Koji Ohkitani
Keyword(s):  
Two Dimensional ◽  
Inviscid Fluids

Directed fluid sheets

1976 ◽  
Vol 347 (1651) ◽  
pp. 447-473 ◽  
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Steady Motion ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Inviscid Fluids ◽  
Two Dimensional Flows

This paper is concerned mainly with incompressible inviscid fluid sheets but the incompressible linearly viscous fluid sheet is also considered. Our development is based on a direct formulation using the two dimensional theory of directed media called Cosserat surfaces . The first part of the paper deals with the formulation of appropriate nonlinear equations (which may include the effects of gravity and surface tension) governing the two dimensional motion of incompressible inviscid media for two categories, namely those ( a ) for two dimensional flows confined to a plane perpendicular to a specified direction and ( b ) for propagation of fairly long waves in a stream of variable initial depth. The latter development is a generalization of an earlier direct formulation of a theory of water waves when the fixed bottom of the stream is level (Green, Laws & Naghdi 1974). In the second part of the paper, special attention is given to a demonstration of the relevance and applicability of the present direct formulation to a variety of two dimensional problems of inviscid fluid sheets. These include, among others, the steady motion of a class of two-dimensional flows in a stream of finite depth in which the bed of the stream may change from one constant level to another, the related problem of hydraulic jumps, and a class of exact solutions which characterize the main features of the time-dependent free surface flows in the three dimensional theory of incompressible inviscid fluids.

scholarly journals Two-dimensional turbulence in inviscid fluids or guiding center plasmas

1975 ◽  
Vol 18 (7) ◽  
pp. 803 ◽  
Author(s):  
C. E. Seyler ◽  
Yehuda Salu ◽  
David Montgomery ◽  
Georg Knorr
Keyword(s):  
Two Dimensional ◽  
Inviscid Fluids

scholarly journals Withdrawal from a two-layer inviscid fluid in a duct

1998 ◽  
Vol 361 ◽  
pp. 275-296 ◽  
Author(s):  
LAWRENCE K. FORBES ◽  
GRAEME C. HOCKING
Keyword(s):  
Froude Number ◽  
Numerical Solutions ◽  
Operating Conditions ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Two Fluids ◽  
Inviscid Fluids ◽  
Integral Equation Formulation ◽  
Arbitrary Position ◽  
Subcritical Solutions

The steady simultaneous withdrawal of two inviscid fluids of different densities in a duct of finite height is considered. The flow is two-dimensional, and the fluids are removed by means of a line sink at some arbitrary position within the duct. It is assumed that the interface between the two fluids is drawn into the sink, and that the flow is uniform far upstream. A numerical method based on an integral equation formulation yields accurate solutions to the problem, and it is shown that under normal operating conditions, there is a solution for each value of the upstream interface height. Numerical solutions suggest that limiting configurations exist, in which the interface is drawn vertically into the sink. The appropriate hydraulic Froude number is derived for this situation, and it is shown that a continuum of solutions exists that are supercritical with respect to this Froude number. An isolated branch of subcritical solutions is also presented.

Instability, coalescence and fission of finite-area vortex structures

1973 ◽  
Vol 61 (2) ◽  
pp. 219-243 ◽  
Author(s):  
J. P. Christiansen ◽  
N. J. Zabusky
Keyword(s):  
Growth Rate ◽  
Small Scale ◽  
Two Dimensional ◽  
Large Area ◽  
Finite Area ◽  
Inviscid Fluids ◽  
Von Karman ◽  
Long Time ◽  
The Stability ◽  
Von Kármán

We have made computational experiments to study the stability and long-time evolution of two-dimensional wakes. We have used the VORTEX code, a finite-difference realization of two-dimensional motions in incompressible inviscid fluids. In the first experiment an initial shear-unstable triangular velocity profile evolves into a non-homogeneous, finite-area, asymmetric vortex array and like-signed regions attract andfuse(or coalesce). Enhanced transport across the profile is due to ‘capture’ and convection of small-scale vortex regions by larger opposite-signed vortex regions. In the following experiments we study the stability of an asymmetric four-vortexfinite-areasystem corresponding to a von Kármán street of point vortices. Here the critical parameter isb/a, the initial transverse-to-longitudinal separation ratio of vortex centres. At\[ b/a = 0.281 \]the four-vortex system is stable and we observe that large-area vortex regions develop elliptical (m= 2), triangular (m= 3), etc. surface modes owing to mutual interactions. Atb/a= 0 the measured growth rate is smaller than that for the corresponding von Kármán system and atb/a= 0·6 the measured growth rate is larger. Atb/a= 0 one vortex undergoes fission in the high-shear field produced by two nearest-neighbour opposite-signed vortex regions. Heuristic comparisons are made with the two-dimensional tunnel experiments of Taneda and others.

scholarly journals Two-dimensional turbulence in inviscid fluids or guiding center plasmas

1975 ◽  
Author(s):  
Jr, C. E. Seyler ◽  
Y. Salu ◽  
D. Montgomery ◽  
G. Knorr
Keyword(s):  
Two Dimensional ◽  
Inviscid Fluids

Numerical studies of two-dimensional Faraday oscillations of inviscid fluids

2000 ◽  
Vol 402 ◽  
pp. 1-32 ◽  
Author(s):  
JEFF WRIGHT ◽  
STEVE YON ◽  
C. POZRIKIDIS
Keyword(s):  
Integral Method ◽  
Density Ratio ◽  
Extended Period ◽  
Vortex Sheet ◽  
Boundary Integral ◽  
The Other ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Inviscid Fluids ◽  
Mathieu’S Equation

The dynamics of two-dimensional standing periodic waves at the interface between two inviscid fluids with different densities, subject to monochromatic oscillations normal to the unperturbed interface, is studied under normal- and low-gravity conditions. The motion is simulated over an extended period of time, or up to the point where the interface intersects itself or the curvature becomes very large, using two numerical methods: a boundary-integral method that is applicable when the density of one fluid is negligible compared to that of the other, and a vortex-sheet method that is applicable to the more general case of arbitrary densities. The numerical procedure for the boundary-integral formulation uses a global isoparametric parametrization based on cubic splines, whereas the numerical method for the vortex-sheet formulation uses a local boundary-element parametrization based on circular arcs. Viscous dissipation is simulated by means of a phenomenological damping coefficient added to the Bernoulli equation or to the evolution equation for the strength of the vortex sheet. A comparative study reveals that the boundary-integral method is generally more accurate for simulating the motion over an extended period of time, but the vortex-sheet formulation is significantly more efficient. In the limit of small deformations, the numerical results are in excellent agreement with those predicted by the linear model expressed by Mathieu's equation, and are consistent with the predictions of the Floquet stability analysis. Nonlinear effects for non-infinitesimal amplitudes are manifested in several ways: deviation from the predictions of Mathieu's equation, especially at the extremes of the interfacial oscillation; growth of harmonic waves with wavenumbers in the unstable regimes of the Mathieu stability diagram; formation of complex interfacial structures including paired travelling waves; entrainment and mixing by ejection of droplets from one fluid into the other; and the temporal period tripling observed recently by Jiang et al. (1998). Case studies show that the surface tension, density ratio, and magnitude of forcing play a significant role in determining the dynamics of the developing interfacial patterns.

scholarly journals Relaxation methods applied to engineering problems XII. Fluid motions characterized by 'free' stream-lines

1946 ◽  
Vol 240 (815) ◽  
pp. 117-161 ◽  
Keyword(s):  
Conformal Transformation ◽  
Free Stream ◽  
Two Dimensional ◽  
Relaxation Methods ◽  
Inviscid Fluids ◽  
Engineering Problems ◽  
Steady Motions ◽  
Stream Lines ◽  
In Virtue Of ◽  
Hydrodynamical Theory

This paper deals with problems which are like the percolation problems of Part VII (Shaw & Southwell 1941) in that a double condition, imposed at a boundary initially unknown, replaces the more usual single condition at a specified boundary. They relate to ‘free’ stream-lines in the hydrodynamical theory of inviscid fluids. For plane two-dimensional (steady) motions, the device of conformal transformation has led in the hands of Helmholtz, Kirchhoff and Rayleigh to a variety of solutions; but up to the present it has not taken account of gravity, and it would not seem capable of extension to motions characterized by axial symmetry. Relaxation Methods, in virtue of their tentative approach, here deal successfully with some problems hitherto unsolved.

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