Three-Dimensional Spatial Normal Modes in Compressible Boundary Layers

2006 ◽  
Author(s):  
Anatoli Tumin
Keyword(s):  
Boundary Layers ◽  
Three Dimensional ◽  
Normal Modes ◽  
Compressible Boundary Layers

Three-dimensional spatial normal modes in compressible boundary layers

2007 ◽  
Vol 586 ◽  
pp. 295-322 ◽  
Author(s):  
ANATOLI TUMIN
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Three Dimensional ◽  
Normal Modes ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Compressible Boundary Layers ◽  
Partial Data ◽  
Finite Growth ◽  
The Cauchy Problem

Three-dimensional spatially growing perturbations in a two-dimensional compressible boundary layer are considered within the scope of linearized Navier–Stokes equations. The Cauchy problem is solved under the assumption of a finite growth rate of the disturbances. It is shown that the solution can be presented as an expansion into a biorthogonal eigenfunction system. The result can be used in a decomposition of flow fields derived from computational studies when pressure, temperature, and all the velocity components, together with some of their derivatives, are available. The method can also be used if partial data are available when a priori information may be utilized in the decomposition algorithm.

ON NONPARALLEL STABILITY OF THREE-DIMENSIONAL COMPRESSIBLE BOUNDARY LAYERS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1503-1506
Author(s):  
JIXUE LIU ◽  
DENGBIN TANG ◽  
GUOXING ZHU
Keyword(s):  
Boundary Layers ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Method ◽  
Curvature Variation ◽  
Compressible Boundary Layers ◽  
Curvilinear Coordinate ◽  
The Difference

Nonparallel stability of the compressible boundary layers for three-dimensional configurations having large curvature variation on the surface is investigated by using the parabolic stability equations, which are derived from the Navier-Stokes equations in the curvilinear coordinate system. The difference schemes with fourth-order accuracy can be used in the entire computational regions. The global method is combined with the local method using a new iterative formula, thus more precise eigenvalues are obtained, and fast convergences are achieved. Computed curves of the amplification factor and shape functions of disturbances show clearly variable process of the flow stability, and agree well with other available results.

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