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Abstract
In an incompressible fluid flow, streamline patterns and their bifurcations are investigated close to wall for twodimensional system and close to free and viscous surfaces in threedimensional system. Expanding the velocity field in a Taylor series, we conduct a local analysis at the given expansion point. Applying the boundary conditions, some relations are obtained among the coefficients of the expansions. Series of coordinate transformations, which preserves the boundary conditions, are used to reduce the number of coefficients. Finally, using the normal form and unfolding theory, the velocity field is analysed structurally and bifurcation diagrams are obtained.
First, twodimensional viscous flow close to wall for nonsimple degenerate critical point is considered depending on threeparameter space. Second, threedimensional axisymmetric, viscous and steady flow is analysed close to free and viscous surfaces into three situations: Local analysis close to center axis; away from the axis and close to a stationary wall. Next, in the absence of axisymmetric condition, threedimensional viscous flow is consider close to a free surface.
As an application of the bifurcation diagrams for threedimensional axisymmetric viscous flow, three different shaped container driven by a rotating top disk is considered. Using a spectral collocation method, a code is constructed to obtain the meridional and swirl velocities. In a result of this code, all structural changes on the streamline patterns are observed and the occurring bifurcations are determined. These bifurcations are compared with the bifurcations obtained from topologically.
First, twodimensional viscous flow close to wall for nonsimple degenerate critical point is considered depending on threeparameter space. Second, threedimensional axisymmetric, viscous and steady flow is analysed close to free and viscous surfaces into three situations: Local analysis close to center axis; away from the axis and close to a stationary wall. Next, in the absence of axisymmetric condition, threedimensional viscous flow is consider close to a free surface.
As an application of the bifurcation diagrams for threedimensional axisymmetric viscous flow, three different shaped container driven by a rotating top disk is considered. Using a spectral collocation method, a code is constructed to obtain the meridional and swirl velocities. In a result of this code, all structural changes on the streamline patterns are observed and the occurring bifurcations are determined. These bifurcations are compared with the bifurcations obtained from topologically.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  194 
Publication status  Published  2016 
Series  DTU Compute PHD2015 

Number  379 
ISSN  09093192 
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Projects
 1 Finished

Topological fluid dynamics: Symmetry breaking and fluid interfaces
Balci, A., Brøns, M., Henriksen, C., Hartnack, J. N. & Blackmore, D.
01/09/2012 → 19/11/2015
Project: PhD