42 research outputs found
The rise of fully turbulent flow
Over a century of research into the origin of turbulence in wallbounded shear
flows has resulted in a puzzling picture in which turbulence appears in a
variety of different states competing with laminar background flow. At slightly
higher speeds the situation changes distinctly and the entire flow is
turbulent. Neither the origin of the different states encountered during
transition, nor their front dynamics, let alone the transformation to full
turbulence could be explained to date. Combining experiments, theory and
computer simulations here we uncover the bifurcation scenario organising the
route to fully turbulent pipe flow and explain the front dynamics of the
different states encountered in the process. Key to resolving this problem is
the interpretation of the flow as a bistable system with nonlinear propagation
(advection) of turbulent fronts. These findings bridge the gap between our
understanding of the onset of turbulence and fully turbulent flows.Comment: 31 pages, 9 figure
Theoretical perspective on the route to turbulence in a pipe
The route to turbulence in pipe flow is a complex, nonlinear, spatiotemporal process for which an increasingly clear theoretical understanding has emerged. This understanding is explained to the reader in several steps, exploiting analogies to co-existing thermodynamic phases and to excitable and bistable media. In the end, simple equations encapsulating the keys physical properties of pipe turbulence provide a comprehensive picture of all large-scale states and stages of the transition process. Important among these are metastable localized puffs, localized edge states, puff splitting and interactions between puffs, the critical point for the onset of sustained turbulence via spatiotemporal intermittency (directed percolation), and finally the rise of fully turbulent flow in the form of expanding weak and strong turbulent slugs
Turbulent-laminar patterns in shear flows without walls
Turbulent-laminar intermittency, typically in the form of bands and spots, is
a ubiquitous feature of the route to turbulence in wall-bounded shear flows.
Here we study the idealised shear between stress-free boundaries driven by a
sinusoidal body force and demonstrate quantitative agreement between turbulence
in this flow and that found in the interior of plane Couette flow -- the region
excluding the boundary layers. Exploiting the absence of boundary layers, we
construct a model flow that uses only four Fourier modes in the shear direction
and yet robustly captures the range of spatiotemporal phenomena observed in
transition, from spot growth to turbulent bands and uniform turbulence. The
model substantially reduces the cost of simulating intermittent turbulent
structures while maintaining the essential physics and a direct connection to
the Navier-Stokes equations.
We demonstrate the generic nature of this process by introducing stress-free
equivalent flows for plane Poiseuille and pipe flows which again capture the
turbulent-laminar structures seen in transition.Comment: 13 pages, 9 figure
Transition to turbulence in pulsating pipe flow
Fluid flows in nature and applications are frequently subject to periodic
velocity modulations. Surprisingly, even for the generic case of flow through a
straight pipe, there is little consensus regarding the influence of pulsation
on the transition threshold to turbulence: while most studies predict a
monotonically increasing threshold with pulsation frequency (i.e. Womersley
number, ), others observe a decreasing threshold for identical
parameters and only observe an increasing threshold at low . In the
present study we apply recent advances in the understanding of transition in
steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we
find that the first instability encountered is subcritical (i.e. requiring
finite amplitude disturbances) and gives rise to localized patches of
turbulence ("puffs") analogous to steady pipe flow. By monitoring the impact of
pulsation on the lifetime of turbulence we map the onset of turbulence in
parameter space. Transition in pulsatile flow can be separated into three
regimes. At small Womersley numbers the dynamics are dominated by the decay
turbulence suffers during the slower part of the cycle and hence transition is
delayed significantly. As shown in this regime thresholds closely agree with
estimates based on a quasi steady flow assumption only taking puff decay rates
into account. The transition point predicted in the zero limit equals
to the critical point for steady pipe flow offset by the oscillation Reynolds
number. In the high frequency limit puff lifetimes are identical to those in
steady pipe flow and hence the transition threshold appears to be unaffected by
flow pulsation. In the intermediate frequency regime the transition threshold
sharply drops (with increasing ) from the decay dominated (quasi
steady) threshold to the steady pipe flow level
Speed and structure of turbulent fronts in pipe flow
Using extensive direct numerical simulations, the dynamics of
laminar-turbulent fronts in pipe flow is investigated for Reynolds numbers
between and . We here investigate the physical distinction
between the fronts of weak and strong slugs both by analysing the turbulent
kinetic energy budget and by comparing the downstream front motion to the
advection speed of bulk turbulent structures. Our study shows that weak
downstream fronts travel slower than turbulent structures in the bulk and
correspond to decaying turbulence at the front. At the
downstream front speed becomes faster than the advection speed, marking the
onset of strong fronts. In contrast to weak fronts, turbulent eddies are
generated at strong fronts by feeding on the downstream laminar flow. Our study
also suggests that temporal fluctuations of production and dissipation at the
downstream laminar-turbulent front drive the dynamical switches between the two
types of front observed up to .Comment: 14 pages, accepted for publication in Journal of Fluid Mechanic
Transition to subcritical turbulence in a tokamak plasma
Tokamak turbulence, driven by the ion-temperature gradient and occurring in
the presence of flow shear, is investigated by means of local, ion-scale,
electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of
the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A
parameter scan in the local values of the ion-temperature gradient and flow
shear is performed. It is demonstrated that the experimentally observed state
is near the stability threshold and that this stability threshold is nonlinear:
sheared turbulence is subcritical, i.e. the system is formally stable to small
perturbations, but, given a large enough initial perturbation, it transitions
to a turbulent state. A scenario for such a transition is proposed and
supported by numerical results: close to threshold, the nonlinear saturated
state and the associated anomalous heat transport are dominated by long-lived
coherent structures, which drift across the domain, have finite amplitudes, but
are not volume filling; as the system is taken away from the threshold into the
more unstable regime, the number of these structures increases until they
overlap and a more conventional chaotic state emerges. Whereas this appears to
represent a new scenario for transition to turbulence in tokamak plasmas, it is
reminiscent of the behaviour of other subcritically turbulent systems, e.g.
pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic
Dynamics of viscoelastic pipe flow in the maximum drag reduction limit
Polymer additives can substantially reduce the drag of turbulent flows and
the upper limit, the so called "maximum drag reduction" (MDR) asymptote is
universal, i.e. independent of the type of polymer and solvent used. Until
recently, the consensus was that, in this limit, flows are in a marginal state
where only a minimal level of turbulence activity persists. Observations in
direct numerical simulations using minimal sized channels appeared to support
this view and reported long "hibernation" periods where turbulence is
marginalized. In simulations of pipe flow we find that, indeed, with increasing
Weissenberg number (Wi), turbulence expresses long periods of hibernation if
the domain size is small. However, with increasing pipe length, the temporal
hibernation continuously alters to spatio-temporal intermittency and here the
flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an
increase in Wi, the flow fully relaminarises, in agreement with recent
experiments. At even larger Wi, a different instability is encountered causing
a drag increase towards MDR. Our findings hence link earlier minimal flow unit
simulations with recent experiments and confirm that the addition of polymers
initially suppresses Newtonian turbulence and leads to a reverse transition.
The MDR state on the other hand results from a separate instability and the
underlying dynamics corresponds to the recently proposed state of
elasto-inertial-turbulence (EIT).Comment: 18 pages, 5 figure
Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence
We present a new experimental set-up that creates a shear flow with zero mean
advection velocity achieved by counterbalancing the nonzero streamwise pressure
gradient by moving boundaries, which generates plane Couette-Poiseuille flow.
We carry out the first experimental results in the transitional regime for this
flow. Using flow visualization we characterize the subcritical transition to
turbulence in Couette-Poiseuille flow and show the existence of turbulent spots
generated by a permanent perturbation. Due to the zero mean advection velocity
of the base profile, these turbulent structures are nearly stationary. We
distinguish two regions of the turbulent spot: the active, turbulent core,
which is characterized by waviness of the streaks similar to traveling waves,
and the surrounding region, which includes in addition the weak undisturbed
streaks and oblique waves at the laminar-turbulent interface. We also study the
dependence of the size of these two regions on Reynolds number. Finally, we
show that the traveling waves move in the downstream (Poiseuille).Comment: 17 pages, 15 figure
Turbulence in a localized puff in a pipe
This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this recordWe have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snapshots) of the velocity fields acquired over T = 2000D/U time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross-plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this “fully-developed turbulent flash” is very narrow being about two pipe diameters long