Numerical exterior algebra and the compound matrix method

2002 ◽  
Vol 92 (2) ◽  
pp. 197-232 ◽  
Author(s):  
Leanne Allen ◽  
Thomas J. Bridges
Keyword(s):  
Matrix Method ◽  
Exterior Algebra ◽  
Compound Matrix Method ◽  
Compound Matrix

scholarly journals Compound matrix method for eigenvalue problems in multiple connected domains

1992 ◽  
Vol 8 (11) ◽  
pp. 811-818 ◽  
Author(s):  
N. R. Anturkar ◽  
T. C. Papanastasiou ◽  
J. O. Wilkes
Keyword(s):  
Matrix Method ◽  
Eigenvalue Problems ◽  
Compound Matrix Method ◽  
Compound Matrix

scholarly journals Generalized compound matrix method

2006 ◽  
Vol 19 (5) ◽  
pp. 458-463 ◽  
Author(s):  
V.V. Gubernov ◽  
H.S. Sidhu ◽  
G.N. Mercer
Keyword(s):  
Matrix Method ◽  
Compound Matrix Method ◽  
Compound Matrix

On the linear stability of spiral flow between rotating cylinders

1982 ◽  
Vol 382 (1782) ◽  
pp. 83-102 ◽  
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Stability Boundary ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
Compound Matrix Method ◽  
Compound Matrix ◽  
High Reynolds ◽  
The Stability ◽  
Axisymmetric Disturbances

A numerical study is made of the effects of both axisymmetric and non-axisymmetric disturbances on the stability of spiral flow between rotating cylinders. If we let Ω 1 and Ω 2 be the angular speeds of the inner and outer cylinders, and R 1 and R 2 be their respective radii, then for fixed values of η = R 1 / R 2 and μ = Ω 2 / Ω 1 , the onset of instability depends on both the Taylor number T and the axial Reynolds number R . Here R is based on the gap width between the cylinders and the average axial velocity of the basic flow, while T is based on the average angular speeds of the cylinders. Using the compound matrix method, we have computed the complete stability boundary in the R , T -plane for axisymmetric disturbances with η = 0.95 and μ = 0. We find that, for sufficiently high Reynolds numbers, there are two distinct axisymmetric modes corresponding to the usual shear and rotational instabilities. We have also obtained the stability boundaries for non-axisymmetric disturbances for R ≼ 6000 for η = 0.95 and 0.77 with μ = 0. These last results are found to be in substantial agreement with the experimental observations of Snyder (1962, 1965), Nagib (1972) and Mavec (1973) in the low and moderate axial Reynolds number régimes.

Effects of surface film on the linear stability of an air–sea interface

1998 ◽  
Vol 357 ◽  
pp. 59-81 ◽  
Author(s):  
ØYVIND SAETRA
Keyword(s):  
Linear Stability ◽  
Surface Film ◽  
Vertical Component ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Pressure Work ◽  
Compound Matrix Method ◽  
Compound Matrix ◽  
The Stability ◽  
Log Linear

The linear stability of turbulent shear flow over a film-covered sea surface is studied theoretically. A compound matrix method (Wheless & Csanady 1993), is used to solve the eigenvalue problem numerically. The numerical method has been adjusted to a coupled air–sea system. In the stability problem the vertical component of the turbulent Reynolds stress has been taken into account. As pointed out by Wheless & Csanady, the second derivative of the traditional log–linear wind profile has a rather extreme behaviour near the matching point of the linear and logarithmic part. To improve the model, a new profile is calculated based on an eddy viscosity distribution for channel flow (Quarmby & Anand 1969), which has continuous derivatives all the way down to the surface. Calculations of the wave growth rates corresponds well with earlier theoretical results as well as laboratory measurements. The energy flux from the air to the sea caused by the pressure work at the surface has been calculated. An intriguing result obtained here is that this flux seems to be strongly dependent on the elastic property of the surface film. The flux attains a maximum for finite values of the film elasticity parameter.

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