Calculations of rotational flows using stream function

1989 ◽  
Author(s):  
M. HAFEZ ◽  
C. YAM ◽  
K. TANG ◽  
H. DWYER
Keyword(s):  
Stream Function ◽  
Rotational Flows

Simple rotational flows

1977 ◽  
Vol 82 (4) ◽  
pp. 687-703 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Boundary Layers ◽  
Nonlinear Equations ◽  
Stream Function ◽  
Analytical Solutions ◽  
Compressible Flows ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Fluid Density ◽  
Rotational Flows ◽  
Starting Process

The paper develops and discusses some new additions to the available stock of analytical solutions of the nonlinear equations of fluid motion. The motions are steady, two-dimensional and devoid of viscous or other rotational forces (although such forces must have been significant during any starting process). The fluid density is constant.The solutions are in two groups, referred respectively to Cartesian and polar co-ordinates. In both the stream function is of separable form, i.e. expressible as a product of two functions, each dependent on one co-ordinate. A remarkable variety of motions is revealed. Those that are most significant physically are described as bends (rapid transitions from one rectilinear flow to another) or as loops (closed, non-circular, vortex-type flows). The effects of boundary layers at walls or instability are not explored.The paper closes with a mention of some preliminary experiments on loop flows in which all streamlines are ellipses and some discussion of the applicability of bend flows. Generalizations to axisymmetric flows and compressible flows are also mentioned briefly.

New Exact Solutions of Steady Plane Flows of an In Compressible Fluid of Variable Viscosity

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Sobia Younus
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Compressible Fluid ◽  
Variable Viscosity ◽  
Plane Motion ◽  
Transformation Technique ◽  
Vorticity Distribution ◽  
New Exact Solutions ◽  
Steady Plane ◽  
Uniform Stream

<span>Some new exact solutions to the equations governing the steady plane motion of an in compressible<span> fluid of variable viscosity for the chosen form of the vorticity distribution are determined by using<span> transformation technique. In this case the vorticity distribution is proportional to the stream function<span> perturbed by the product of a uniform stream and an exponential stream<br /><br class="Apple-interchange-newline" /></span></span></span></span>

scholarly journals On rotational flows with discontinuous vorticity beneath steady water waves near stagnation

2021 ◽  
Vol 912 ◽  
Author(s):  
Lin Chen ◽  
Biswajit Basu ◽  
Calin-I. Martin
Keyword(s):  
Water Waves ◽  
Rotational Flows

Abstract

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

Nonlinear hydrodynamic stability of some simple rotational flows

1982 ◽  
Vol 71 (2) ◽  
pp. 282-294 ◽  
Author(s):  
S. Pierini ◽  
E. Salusti
Keyword(s):  
Hydrodynamic Stability ◽  
Rotational Flows

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

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