Asymptotic description of transitional and turbulent flows: effects of surface roughness on the boundary layer and the evolution of coherent structures in free shear flows
File(s)
Author(s)
Katai, Csaba Bence
Type
Thesis
Abstract
In this thesis we investigate, using high-Reynolds-number asymptotic techniques,
three fluid dynamics problems linked to transition and turbulence. The first problem
concerns the impact of spanwise periodic, streamwise elongated surface roughness
elements on the boundary-layer stability. We are mainly interested in their
effects on the so-called lower-branch modes, therefore, the spanwise spacing of
the roughness is chosen to be comparable to the characteristic wavelength of the
instability modes which is on the triple-deck scale. The streamwise length is much
longer, consistent with experimental setups. By appropriate rescaling, a nonlinear
set of boundary-layer equations are derived from the generic triple-deck theory.
As the pressure is completely determined by the roughness shape to leading order,
the governing equations can be solved by an efficient marching method to
compute the streaky flow. The instability of the streaky flow is reduced to a
one-dimensional eigenvalue problem in the spanwise direction. The instability is
found to be controlled by the (spanwise periodic) streamwise wall shear. The numerical
results are then compared to existing experimental data for which a good
qualitative agreement is obtained.
The second problem investigates the nonlinear dynamics of coherent structures in
the turbulent mixing layer. Experimental results have shown that these large-scale
motions share many characteristics with instability waves. Most of the characteristics
can be predicted by a stability analysis of the mean flow. The instantaneous
flow field is decomposed into the mean flow, coherent and incoherent fluctuations.
The problem is closed by applying appropriate turbulence closures to the so-called
modulated Reynolds stress transport equations. The nonlinear critical-layer theory
for laminar-flow instabilities is adapted to develop a mathematical theory
describing the evolution of coherent structures. With the present high-level turbulence
closure model, the effect of fine-grained turbulence on the coherent structures
is shown to appear as novel dispersion as well as anisotropic diffusion, in contrast
to isotropic diffusion in the gradient-type models. The theoretical predictions
capture the main nonlinear features of the coherent structures.
Lastly, we apply an existing weakly-nonlinear theory to the evolution of coherent
structures in the turbulent wake, but unlike previous works, we use a newly observed
non-equilibrium turbulent dissipation scaling law that holds in the region
where energetic coherent structures are present, and is different from that linked
to the classical Richardson–Kolmogorov equilibrium cascade.
three fluid dynamics problems linked to transition and turbulence. The first problem
concerns the impact of spanwise periodic, streamwise elongated surface roughness
elements on the boundary-layer stability. We are mainly interested in their
effects on the so-called lower-branch modes, therefore, the spanwise spacing of
the roughness is chosen to be comparable to the characteristic wavelength of the
instability modes which is on the triple-deck scale. The streamwise length is much
longer, consistent with experimental setups. By appropriate rescaling, a nonlinear
set of boundary-layer equations are derived from the generic triple-deck theory.
As the pressure is completely determined by the roughness shape to leading order,
the governing equations can be solved by an efficient marching method to
compute the streaky flow. The instability of the streaky flow is reduced to a
one-dimensional eigenvalue problem in the spanwise direction. The instability is
found to be controlled by the (spanwise periodic) streamwise wall shear. The numerical
results are then compared to existing experimental data for which a good
qualitative agreement is obtained.
The second problem investigates the nonlinear dynamics of coherent structures in
the turbulent mixing layer. Experimental results have shown that these large-scale
motions share many characteristics with instability waves. Most of the characteristics
can be predicted by a stability analysis of the mean flow. The instantaneous
flow field is decomposed into the mean flow, coherent and incoherent fluctuations.
The problem is closed by applying appropriate turbulence closures to the so-called
modulated Reynolds stress transport equations. The nonlinear critical-layer theory
for laminar-flow instabilities is adapted to develop a mathematical theory
describing the evolution of coherent structures. With the present high-level turbulence
closure model, the effect of fine-grained turbulence on the coherent structures
is shown to appear as novel dispersion as well as anisotropic diffusion, in contrast
to isotropic diffusion in the gradient-type models. The theoretical predictions
capture the main nonlinear features of the coherent structures.
Lastly, we apply an existing weakly-nonlinear theory to the evolution of coherent
structures in the turbulent wake, but unlike previous works, we use a newly observed
non-equilibrium turbulent dissipation scaling law that holds in the region
where energetic coherent structures are present, and is different from that linked
to the classical Richardson–Kolmogorov equilibrium cascade.
Version
Open Access
Date Issued
2020-07
Date Awarded
2020-12
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Wu, Xuesong
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)