Linear instability of the supersonic wake behind a flat plate aligned with a uniform stream

1990 ◽  
Vol 1 (6) ◽  
pp. 327-348 ◽  
Author(s):  
D. T. Papageorgiou
Keyword(s):  
Flat Plate ◽  
Linear Instability ◽  
Supersonic Wake ◽  
Uniform Stream

Linear instability of the wake behind a flat plate placed parallel to a uniform stream

1989 ◽  
Vol 208 ◽  
pp. 67-89 ◽  
Author(s):  
D. T. Papageorgiou ◽  
F. T. Smith
Keyword(s):  
Flat Plate ◽  
Ad Hoc ◽  
Equations Of Motion ◽  
Theoretical Work ◽  
Linear Instability ◽  
Nonlinear Analyses ◽  
Boundary Layer Equations ◽  
Laminar Wake ◽  
High Reynolds ◽  
Uniform Stream

The growth of linear disturbances in the high-Reynolds-number laminar wake of a flat plate aligned with a uniform stream is investigated. The theory is developed rationally by use of appropriate wake profiles which originate at the trailing edge as double Blasius distributions and thereafter satisfy the equations of motion, in contrast to previous theoretical work where model profiles are used. We also emphasize the structures and scales of the instability in order to provide a rational basis for the development of nonlinear analyses as opposed to existing ad hoc ones. Disturbances, in the near wake, respond according to the Rayleigh equation which is considered analytically for short-, long- and neutral-wave solutions. For more general stability characteristics eigensolutions must be obtained numerically. We calculate these at successive wake stations for ‘improved’ basic flow profiles which are obtained as solutions of the wake boundary-layer equations. Our numerical results indicate fairly good agreement with the asymptotic theory and some experimental data (see §7).

scholarly journals Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Hossein Aminikhah ◽  
Somayyeh Kazemi
Keyword(s):  
Boundary Layer ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Method ◽  
Flow Problem ◽  
Spline Method ◽  
B Spline ◽  
Theoretical Considerations ◽  
Uniform Stream

A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error L2-norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.

Nonlinear instability of the wake behind a flat plate placed parallel to a uniform stream

1988 ◽  
Vol 419 (1856) ◽  
pp. 1-28 ◽  
Keyword(s):  
Surface Tension ◽  
Flat Plate ◽  
Euler Equations ◽  
Theoretical Study ◽  
Nonlinear Evolution ◽  
Nonlinear Instability ◽  
Pressure Jump ◽  
Long Wavelength ◽  
Evolution With Time ◽  
Uniform Stream

A theoretical study is presented on nonlinear aspects in the instability of the wake behind an aligned flat plate. This is done in the long-wavelength régime by asymptotic solutions of the unsteady Euler equations, in a rational fashion. In particular, equations are obtained that describe the nonlinear evolution with time and space of the vortex-layer interface formed just downstream of the trailing edge. The instability is found to be driven by a pressure jump across this layer, which has the same form as that arising from surface-tension effects but with a negative (destabilizing) sign. Finite-time breakdown of the solutions is conjectured and analysed. The usefully simplified case of a bounded wake is formulated, analysed and computed numerically, and comparisons are made with experiments, showing qualitative agreement.

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