---
OA_place: publisher
_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."
alternative_title:
- ISTA 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. 2019. doi:<a href="https://doi.org/10.15479/AT:ISTA:6957">10.15479/AT:ISTA:6957</a>
  apa: Paranjape, C. S. (2019). <i>Onset of turbulence in plane Poiseuille flow</i>.
    Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/AT:ISTA:6957">https://doi.org/10.15479/AT:ISTA:6957</a>
  chicago: Paranjape, Chaitanya S. “Onset of Turbulence in Plane Poiseuille Flow.”
    Institute of Science and Technology Austria, 2019. <a href="https://doi.org/10.15479/AT:ISTA:6957">https://doi.org/10.15479/AT:ISTA:6957</a>.
  ieee: C. S. Paranjape, “Onset of turbulence in plane Poiseuille flow,” Institute
    of Science and Technology Austria, 2019.
  ista: Paranjape CS. 2019. Onset of turbulence in plane Poiseuille flow. Institute
    of Science and Technology Austria.
  mla: Paranjape, Chaitanya S. <i>Onset of Turbulence in Plane Poiseuille Flow</i>.
    Institute of Science and Technology Austria, 2019, doi:<a href="https://doi.org/10.15479/AT:ISTA:6957">10.15479/AT:ISTA:6957</a>.
  short: C.S. Paranjape, Onset of Turbulence in Plane Poiseuille Flow, Institute of
    Science and Technology Austria, 2019.
corr_author: '1'
date_created: 2019-10-22T12:08:43Z
date_published: 2019-10-24T00:00:00Z
date_updated: 2026-04-08T07:46:58Z
day: '24'
ddc:
- '532'
degree_awarded: PhD
department:
- _id: BjHo
doi: 10.15479/AT:ISTA:6957
file:
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  date_created: 2019-10-23T09:54:43Z
  date_updated: 2020-07-14T12:47:46Z
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  file_name: Chaitanya_Paranjape_source_files_tex_figures.zip
  file_size: 45828099
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- access_level: open_access
  checksum: 642697618314e31ac31392da7909c2d9
  content_type: application/pdf
  creator: cparanjape
  date_created: 2019-10-23T10:37:09Z
  date_updated: 2020-07-14T12:47:46Z
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  file_name: Chaitanya_Paranjape_Thesis.pdf
  file_size: 19504197
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file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
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: Institute of Science and Technology 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: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2019'
...