scholarly journals On the evolution of laminar to turbulent transition and breakdown to turbulence

2003 ◽  
Vol 7 (2) ◽  
pp. 59-76
Author(s):  
Jovan Jovanovic ◽  
Mira Pashtrapanska
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Correlation Technique ◽  
Equilibrium Solutions ◽  
Laminar To Turbulent Transition ◽  
Transition Criterion ◽  
Flat Plate Boundary Layer

Starting from the basic conservation laws of fluid flow, we investigated transition and breakdown to turbulence of a laminar flat plate boundary layer exposed to small, statistically stationary, two-component, three-dimensional disturbances. The derived equations for the statistical properties of the disturbances are closed using the two-point correlation technique and invariant theory. By considering the equilibrium solutions of the modeled equations, the transition criterion is formulated in terms of a Reynolds number based on the intensity and the length scale of the disturbances. The deduced transition criterion determines conditions that guarantee maintenance of the local equilibrium between the production and the viscous dissipation of the disturbances and therefore the laminar flow regime in the flat plate boundary layer. The experimental and numerical databases for fully developed turbulent channel and pipe flows at different Reynolds numbers were utilized to demonstrate the validity of the derived transition criterion for the estimation of the onset of turbulence in wall-bounded flows.

On the Criterion for the Determination Transition Onset and Breakdown to Turbulence in Wall-Bounded Flows1

2004 ◽  
Vol 126 (4) ◽  
pp. 626-633 ◽  
Author(s):  
J. Jovanovic´ ◽  
M. Pashtrapanska
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Correlation Technique ◽  
Equilibrium Solutions ◽  
Onset Of Turbulence ◽  
Transition Criterion ◽  
Flat Plate Boundary Layer

Starting from the basic conservation laws of fluid flow, we investigated transition and breakdown to turbulence of a laminar flat plate boundary layer exposed to small, statistically stationary, two-component, three-dimensional disturbances. The derived equations for the statistical properties of the disturbances are closed using the two-point correlation technique and invariant theory. By considering the equilibrium solutions of the modeled equations, the transition criterion is formulated in terms of a Reynolds number based on the intensity and the length scale of the disturbances. The deduced transition criterion determines conditions that guarantee maintenance of the local equilibrium between the production and the viscous dissipation of the disturbances and therefore the laminar flow regime in the flat plate boundary layer. The experimental and numerical databases for fully developed turbulent channel and pipe flows at different Reynolds numbers were utilized to demonstrate the validity of the derived transition criterion for the estimation of the onset of turbulence in wall-bounded flows.

Dynamics of three-dimensional coherent structures in a flat-plate boundary layer

1994 ◽  
Vol 275 ◽  
pp. 257-283 ◽  
Author(s):  
Dietmar Rempfer ◽  
Hermann F. Fasel
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Galerkin Projection ◽  
Power Budget ◽  
Energy Flows ◽  
Flat Plate Boundary Layer

An investigation is presented that analyses the energy flows that are connected to the dynamical behaviour of coherent structures in a transitional flat-plate boundary layer. Based on a mathematical description of the three-dimensional coherent structures of this flow as provided by the Karhunen–Loève procedure, energy equations for the coherent structures are derived by Galerkin projection of the Navier–Stokes equations in vorticity transport formulation onto the corresponding basis of eigenfunctions. In a first step, the time-averaged energy balance – showing the energy flows that support the different coherent structures and thus maintain the fluctuations of the velocity field – is considered. In a second step, the instantaneous power budget is investigated for the particularly interesting case of a coherent structure providing a prime contribution to the characteristic spike events of the transitional boundary layer. As this structure shows a strong variation in energy, the question about which mechanisms cause these variations is addressed. Our results show that the occurrence of a spike must be attributed to an autonomous event and cannot be interpreted as just an epiphenomenon of the passage of a Λ-vortex.

scholarly journals Transition Prediction in Incompressible Boundary Layer with Finite-Amplitude Streaks

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2147
Author(s):  
Juan Ángel Martín ◽  
Pedro Paredes
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Plate Boundary ◽  
High Amplitude ◽  
Finite Amplitude ◽  
Critical Conditions ◽  
Bypass Transition ◽  
Transition Delay ◽  
Flat Plate Boundary Layer

Modulating the boundary layer velocity profile is a very promising strategy for achieving transition delay and reducing the friction of the plate. By perturbing the flow with counter-rotating vortices that undergo transient, non-modal growth, streamwise-aligned streaks are formed inside the boundary layer, which have been proved (theoretical and experimentally) to be very robust flow structures. In this paper, we employ efficient numerical methods to perform a parametric stability investigation of the three-dimensional incompressible flat-plate boundary layer with finite-amplitude streaks. For this purpose, the Boundary Region Equations (BREs) are applied to solve the nonlinear downstream evolution of finite amplitude streaks. Regarding the stability analysis, the linear three-dimensional plane-marching Parabolized Stability Equations (PSEs) concept constitutes the best candidate for this task. Therefore, a thorough parametric study is presented, analyzing the instability characteristics with respect to critical conditions of the modified incompressible zero-pressure-gradient flat-plate boundary layer, by means of finite-amplitude linearly optimal and suboptimal disturbances or streaks. The parameter space is extended from low- to high- amplitude streaks, accurately documenting the transition delay for low-amplitude streaks and the amplitude threshold for streak shear layer instability or bypass transition, which drastically displaces the transition front upstream.

Evolution of three-dimensional coherent structures in a flat-plate boundary layer

1994 ◽  
Vol 260 ◽  
pp. 351-375 ◽  
Author(s):  
Dietmar Rempfer ◽  
Hermann F. Fasel
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Complete Information ◽  
Dynamical Behaviour ◽  
Higher Order ◽  
Temporal Behaviour ◽  
Flat Plate Boundary Layer

Using a data base generated by a numerical simulation, the three-dimensional coherent structures of a transitional, spatially evolving boundary layer are determined and their spatio-temporal behaviour is investigated in detail. The coherent structures are calculated by the proper orthogonal decomposition method (POD), which leads to an expansion of the flow field variables into Karhunen-Loéve eigenfunctions. It is shown that the dynamical coherent structures of the flat-plate boundary layer can be described by pairs of eigenfunctions that contain complete information on the spatial evolution of the structures. It is further demonstrated that first-order coherent structures determined by POD correspond to structures that are observed in experiments. In the region of the boundary layer where the spike signals of transition occur, higher-order coherent structures also play an essential role. By considering these higher-order structures as well as their dynamical behaviour in time, a compact description of the flow phenomena in the boundary layer can be obtained. The description of the events occurring at the spike stages of the transitional boundary layer shows, from a coherent structures point of view, striking similarities to the bursting event of fully turbulent boundary layers.

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