Citation
Dumas, Guy (1991) Study of spherical couette flow via 3D spectral simulations: large and narrowgap flows and their transitions. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd04162004103555
Abstract
Incompressible, viscous flows in the spherical gap between a rotating innersphere and a stationary outershell, Spherical Couette Flows (SCF), are studied via direct numerical simulations. The investigation covers both "smallgap" and "largegap" geometries, and is concerned primarily with the first occurrence of transition in those flows. Strong emphasis is put on the physical understanding of the basic flows and their transition mechanisms.
An aliasfree spectral method, based on divergencefree vector expansions for the 3D velocity field in spherical coordinates, is developed. The vector expansions are constructed with Chebyshev polynomials in the radial direction and Vector Spherical Harmonics for the two angular directions. Accuracy and spectral convergence of the resulting initialvalue code are thoroughly tested. Threedimensional transitional flows in both narrowgaps and largegaps as well as axisymmetric transitions in moderategaps are simulated.
For smallgap SCF's, this study shows that the formation of Taylorvortices at transition is a deterministic process and not the result of the instability of initial perturbations. The formation process involves the subcritical appearance of a saddlestagnation point within the meridional circulation cell in each hemisphere. A minimum lengthscale ratio is shown necessary, and for a given innersphere radius, this leads to a theoretical prediction of the largest gapwidth in which Taylorvortices may form.
This investigation confirms that the first transition in largegap SCF's is caused by a 3D instability of a linear nature. It is found that the process is characterized by very small growthrates of the disturbance and by the absence of a "jump" in the friction torque. The supercritical flow is a complexstructured, laminar, timeperiodic flow that exhibits traveling azimuthalwaves. The physical mechanism responsible for the largegap transition is shown to be related to a shear instability of the "radialazimuthal jet" that develops at the equator of the basic flow. A physical model is proposed in which that jet is viewed as a sequence of adjacent "fanspreading quasi2D plane jets". Predictions from the model are presented and verified from the computed unstable disturbance field. Extension of the model to the transition toward waviness in the TaylorCouette flow, the Gortlervortex flow and the Deanvortex flow is proposed.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Couette flows; DNS; gap classification; hydrodynamic instability; largegap flows; NavierStokes; Spectral methods; Spherical coordinates; Taylor vortex formation; TaylorGortler vortex flow; transition 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Mechanical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  30 November 1990 
NonCaltech Author Email:  gdumas (AT) gmc.ulaval.ca 
Record Number:  CaltechETD:etd04162004103555 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd04162004103555 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1397 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  16 Apr 2004 
Last Modified:  26 Dec 2012 02:37 
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