---
_id: '6957'
abstract:
- lang: eng
text: "In many shear flows like pipe flow, plane Couette flow, plane Poiseuille
flow, etc. turbulence emerges subcritically. Here, when subjected to strong enough
perturbations, the flow becomes turbulent in spite of the laminar base flow being
linearly stable. The nature of this instability has puzzled the scientific community
for decades. At onset, turbulence appears in localized patches and flows are spatio-temporally
intermittent. In pipe flow the localized turbulent structures are referred to
as puffs and in planar flows like plane Couette and channel flow, patches arise
in the form of localized oblique bands. In this thesis, we study the onset of
turbulence in channel flow in direct numerical simulations from a dynamical system
theory perspective, as well as by performing experiments in a large aspect ratio
channel.\r\n\r\nThe aim of the experimental work is to determine the critical
Reynolds number where turbulence first becomes sustained. Recently, the onset
of turbulence has been described in analogy to absorbing state phase transition
(i.e. directed percolation). In particular, it has been shown that the critical
point can be estimated from the competition between spreading and decay processes.
Here, by performing experiments, we identify the mechanisms underlying turbulence
proliferation in channel flow and find the critical Reynolds number, above which
turbulence becomes sustained. Above the critical point, the continuous growth
at the tip of the stripes outweighs the stochastic shedding of turbulent patches
at the tail and the stripes expand. For growing stripes, the probability to decay
decreases while the probability of stripe splitting increases. Consequently, and
unlike for the puffs in pipe flow, neither of these two processes is time-independent
i.e. memoryless. Coupling between stripe expansion and creation of new stripes
via splitting leads to a significantly lower critical point ($Re_c=670+/-10$)
than most earlier studies suggest. \r\n\r\nWhile the above approach sheds light
on how turbulence first becomes sustained, it provides no insight into the origin
of the stripes themselves. In the numerical part of the thesis we investigate
how turbulent stripes form from invariant solutions of the Navier-Stokes equations.
The origin of these turbulent stripes can be identified by applying concepts from
the dynamical system theory. In doing so, we identify the exact coherent structures
underlying stripes and their bifurcations and how they give rise to the turbulent
attractor in phase space. We first report a family of localized nonlinear traveling
wave solutions of the Navier-Stokes equations in channel flow. These solutions
show structural similarities with turbulent stripes in experiments like obliqueness,
quasi-streamwise streaks and vortices, etc. A parametric study of these traveling
wave solution is performed, with parameters like Reynolds number, stripe tilt
angle and domain size, including the stability of the solutions. These solutions
emerge through saddle-node bifurcations and form a phase space skeleton for the
turbulent stripes observed in the experiments. The lower branches of these TW
solutions at different tilt angles undergo Hopf bifurcation and new solutions
branches of relative periodic orbits emerge. These RPO solutions do not belong
to the same family and therefore the routes to chaos for different angles are
different. \r\n\r\nIn shear flows, turbulence at onset is transient in nature.
\ Consequently,turbulence can not be tracked to lower Reynolds numbers, where
the dynamics may simplify. Before this happens, turbulence becomes short-lived
and laminarizes. In the last part of the thesis, we show that using numerical
simulations we can continue turbulent stripes in channel flow past the 'relaminarization
barrier' all the way to their origin. Here, turbulent stripe dynamics simplifies
and the fluctuations are no longer stochastic and the stripe settles down to a
relative periodic orbit. This relative periodic orbit originates from the aforementioned
traveling wave solutions. Starting from the relative periodic orbit, a small increase
in speed i.e. Reynolds number gives rise to chaos and the attractor dimension
sharply increases in contrast to the classical transition scenario where the instabilities
affect the flow globally and give rise to much more gradual route to turbulence."
accept: '1'
alternative_title:
- IST Austria Thesis
article_processing_charge: No
author:
- first_name: Chaitanya S
full_name: Paranjape, Chaitanya S
id: 3D85B7C4-F248-11E8-B48F-1D18A9856A87
last_name: Paranjape
citation:
ama: Paranjape CS. *Onset of Turbulence in Plane Poiseuille Flow*. IST Austria;
2019. doi:10.15479/AT:ISTA:6957
apa: Paranjape, C. S. (2019). *Onset of turbulence in plane Poiseuille flow*.
IST Austria. https://doi.org/10.15479/AT:ISTA:6957
chicago: Paranjape, Chaitanya S. *Onset of Turbulence in Plane Poiseuille Flow*.
IST Austria, 2019. https://doi.org/10.15479/AT:ISTA:6957.
ieee: C. S. Paranjape, *Onset of turbulence in plane Poiseuille flow*. IST
Austria, 2019.
ista: Paranjape CS. 2019. Onset of turbulence in plane Poiseuille flow, IST Austria,
138p.
mla: Paranjape, Chaitanya S. *Onset of Turbulence in Plane Poiseuille Flow*.
IST Austria, 2019, doi:10.15479/AT:ISTA:6957.
short: C.S. Paranjape, Onset of Turbulence in Plane Poiseuille Flow, IST Austria,
2019.
date_created: 2019-10-22T12:08:43Z
date_published: 2019-10-24T00:00:00Z
date_updated: 2019-11-28T09:01:16Z
day: '24'
ddc:
- '532'
department:
- _id: BjHo
doi: 10.15479/AT:ISTA:6957
file:
- access_level: closed
content_type: application/zip
creator: cparanjape
date_created: 2019-10-23T09:54:43Z
date_updated: 2019-10-24T06:21:18Z
file_id: '6962'
file_name: Chaitanya_Paranjape_source_files_tex_figures.zip
file_size: 45828099
open_access: 0
relation: source_file
request_a_copy: 0
- access_level: open_access
content_type: application/pdf
creator: cparanjape
date_created: 2019-10-23T10:37:09Z
date_updated: 2019-10-23T10:37:09Z
file_id: '6963'
file_name: Chaitanya_Paranjape_Thesis.pdf
file_size: 19504197
open_access: 1
relation: main_file
success: 1
file_date_updated: 2019-10-24T06:21:18Z
keyword:
- Instabilities
- Turbulence
- Nonlinear dynamics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: '138'
publication_identifier:
eissn:
- 2663-337X
publication_status: published
publisher: IST Austria
status: public
supervisor:
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
title: Onset of turbulence in plane Poiseuille flow
type: dissertation
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...