scholarly journals Steady three-dimensional rotational flows : an approach via two stream functions and Nash–Moser iteration

2019 ◽  
Vol 12 (5) ◽  
pp. 1225-1258 ◽  
Author(s):  
Boris Buffoni ◽  
Erik Wahlén
Keyword(s):  
Three Dimensional ◽  
Moser Iteration ◽  
Rotational Flows ◽  
Stream Functions

NESTED INVARIANT 3-TORI EMBEDDED IN A SEA OF CHAOS IN A QUASIPERIODIC FLUID FLOW

2009 ◽  
Vol 19 (07) ◽  
pp. 2181-2191 ◽  
Author(s):  
HOPE L. WEISS ◽  
ANDREW J. SZERI
Keyword(s):  
Fixed Point ◽  
Fluid Flow ◽  
Cross Sections ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Elliptic Type ◽  
Two Phase ◽  
Dimensional Phase Space ◽  
Hyperbolic Fixed Point ◽  
Stream Functions

Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincaré sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincaré cross-section. This framework has applications to tidal and other mixing problems of geophysical interest.

On the Calculation of Three-Dimensional Divergent and Rotational Flow in Turbomachines

1977 ◽  
Vol 99 (1) ◽  
pp. 187-196
Author(s):  
M. Ribaut
Keyword(s):  
Boundary Layers ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Direct Calculation ◽  
Rotational Flow ◽  
Vortex System ◽  
Vortex Sheets ◽  
Rotational Flows ◽  
Simplifying Assumptions ◽  
Main Effects

This study deals with the calculation of the three-dimensional steady flow of a compressible and viscous fluid through a turbomachine. Using the potential theory, a quasi three-dimensional method is developed, which reduces the simplifying assumptions and yields high numerical accuracy. The method includes all main effects induced by the primary vortex system, in particular the influence of the casing and blade boundary layers on the cascade circulation. The use of two vortex sheets, representing the boundary surface, makes the calculation of flows having strong developed or separated boundary layers possible and allows a direct calculation of the secondary vorticity. Computed divergent and rotational flows are presented and compared with exact solutions or experimental data.

A mixed finite element/control volume model of wind-driven circulation in lakes

2013 ◽  
Vol 5 (1) ◽  
Author(s):  
Victor Podsechin
Keyword(s):  
Control Volume ◽  
Mixed Finite Element ◽  
Surface Wind ◽  
Three Dimensional ◽  
Circulation Model ◽  
Hydrodynamic Equations ◽  
Governing Equations ◽  
Near Surface ◽  
Stream Functions ◽  
Surface Wind Field

AbstractA three-dimensional numerical circulation model is described. The model is based on non-linear hydrodynamic equations, modified according to hydrostatic and Boussinesq approximations. A space-splitting scheme is used for numerical approximations of governing equations. The simple hypothesis on elliptic stream functions shape is utilized to reconstruct the near-surface wind field. The calculated currents correspond reasonably well with observed velocities in different locations lake-wide.

A Three-Dimensional Numerical Method for Turbomachinery Blading

1992 ◽  
Author(s):  
C. W. Gu ◽  
J. Z. Xu ◽  
J. Y. Du
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Stream Function ◽  
Three Dimensional ◽  
Computational Results ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Stream Functions ◽  
Derivatives Of ◽  
Convergent Solution

By inversing one of the stream functions and their principal equations in a three–dimensional flow the equations with the second–order partial derivatives of both the coordinate and another stream function are derived. The corresponding boundary conditions are easily specified. Based on these equations and the boundary conditions the convergent solution for turbomachinery blading is obtained. The computational results show that the method is simple and effective.

Effects of the wall properties on unsteady peristaltic flow of an Eyring–Powell fluid in a three-dimensional rectangular duct

2015 ◽  
Vol 08 (06) ◽  
pp. 1550081 ◽  
Author(s):  
Arshad Riaz ◽  
S. Nadeem ◽  
R. Ellahi
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Peristaltic Flow ◽  
Solution Technique ◽  
Rectangular Duct ◽  
Governing Equations ◽  
Long Wavelength ◽  
Stream Functions

In the present investigation, peristaltic flow of non-Newtonian fluid model (Eyring–Powell) has been taken into consideration in a cross-section of three-dimensional rectangular channel. The flow is taken to be unsteady and incompressible. The observations are made under the limitations of low Reynolds number and long wavelength which helps in reducing the governing equations. The walls of the channel are supposed to be compliant. The obtained equations are nonlinear partial differential equation of second order and have been solved analytically by using series solution technique. The achieved results are then portrayed graphically to see the variation of various emerging parameters on the profile of velocity. The stream functions have also been sketched in order to discuss the trapping behavior of the circular bolus.

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