Two-dimensional absolute instability of a supersonic boundary layer

1988 ◽  
Vol 23 (1) ◽  
pp. 147-150 ◽  
Author(s):  
G. V. Petrov
Keyword(s):  
Boundary Layer ◽  
Supersonic Boundary Layer ◽  
Absolute Instability ◽  
Two Dimensional

Nonlinear Interaction of High-Intensity Disturbances into the Supersonic Boundary Layer

2012 ◽  
Vol 7 (1) ◽  
pp. 38-52
Author(s):  
Natalya Terekhova
Keyword(s):  
Boundary Layer ◽  
Nonlinear Model ◽  
Nonlinear Interaction ◽  
High Intensity ◽  
Plane Waves ◽  
Nonlinear Process ◽  
Supersonic Boundary Layer ◽  
Two Dimensional ◽  
Longitudinal Dynamics ◽  
Second Order Nonlinearity

A nonlinear model of interaction of disturbances in the regime of coupled combinatorial relations is used to explain the dynamics of unstable waves. The model includes effects of self-action and combinatorial interaction of unstable waves. Considered effects in the boundary layer with M = 2 controlled disturbance large enough intensity. In the second case when M = 5,35 examines the interrelationship of two-dimensional perturbations of various nature – vortex and acoustic. Shows the direction of impact of the different components of the nonlinear process. Found that this model of the second order nonlinearity can accurately describe the features of longitudinal dynamics of plane waves

Nonlinear instability of a supersonic boundary layer with two-dimensional roughness

2014 ◽  
Vol 752 ◽  
pp. 497-520 ◽  
Author(s):  
Olaf Marxen ◽  
Gianluca Iaccarino ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Boundary Layer ◽  
Large Amplitude ◽  
Supersonic Boundary Layer ◽  
Secondary Instability ◽  
Secondary Wave ◽  
Nonlinear Instability ◽  
Transient Growth ◽  
Primary Wave ◽  
Two Dimensional ◽  
Lower Amplitude

AbstractNonlinear instability in a supersonic boundary layer at Mach 4.8 with two-dimensional roughness is investigated by means of spatial direct numerical simulations (DNS). It was previously found that an important effect of a two-dimensional roughness is to increase significantly the amplitude of two-dimensional waves downstream of the roughness in a certain frequency band through enhanced instability and transient growth, while waves outside this band are damped. Here, we investigate the nonlinear secondary instability induced by a large-amplitude two-dimensional wave, which has received a significant boost in amplitude from this additional roughness-induced amplification. Both subharmonic and fundamental secondary excitation of the oblique secondary waves are considered. We found that even though the growth rate of the secondary perturbations increases compared to their linear amplification, only in some of the cases was a fully resonant state attained by the streamwise end of the domain. A parametric investigation of the amplitude of the primary wave, the phase difference between the primary and the secondary waves, and the spanwise wavenumber has also been performed. The transient growth experienced by the primary wave was found to not influence the secondary instability for most parameter combinations. For unfavourable phase relations between the primary and the secondary waves, the phase speed of the secondary wave decreases significantly, and this hampers its growth. Finally, we also investigated the strongly nonlinear stage, for which both the primary and the subharmonic secondary waves had a comparable, finite amplitude. In this case, the growth of the primary waves was found to vanish downstream of the transient growth region, resulting in a lower amplitude than in the absence of the large-amplitude secondary wave. This feedback also decreases the amplification rate of the secondary wave.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

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