13,607 research outputs found
Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation
Varying one of the governing parameters of a dynamical system may lead to a
critical transition, where the new stable state is undesirable. In some cases,
there is only a limited range of the bifurcation parameter that corresponds to
that unwanted attractor, while the system runs problem-less otherwise. In this
study, we present experimental results regarding a thermoacoustic system
subject to two consecutive and mirrored supercritical Hopf bifurcations: the
system exhibits high amplitude thermoacoustic limit cycles for intermediate
values of the bifurcation parameter. Changing quickly enough the bifurcation
parameter, it was possible to dodge the unwanted limit cycles. A low-order
model of the complex thermoacoustic system was developed, in order to describe
this interesting transient dynamics. It was afterward used to assess the risk
of exceeding an oscillation amplitude threshold as a function of the rate of
change of the bifurcation parameter
A streamwise-constant model of turbulent pipe flow
A streamwise-constant model is presented to investigate the basic mechanisms
responsible for the change in mean flow occuring during pipe flow transition.
Using a single forced momentum balance equation, we show that the shape of the
velocity profile is robust to changes in the forcing profile and that both
linear non-normal and nonlinear effects are required to capture the change in
mean flow associated with transition to turbulence. The particularly simple
form of the model allows for the study of the momentum transfer directly by
inspection of the equations. The distribution of the high- and low-speed
streaks over the cross-section of the pipe produced by our model is remarkably
similar to one observed in the velocity field near the trailing edge of the
puff structures present in pipe flow transition. Under stochastic forcing, the
model exhibits a quasi-periodic self-sustaining cycle characterized by the
creation and subsequent decay of "streamwise-constant puffs", so-called due to
the good agreement between the temporal evolution of their velocity field and
the projection of the velocity field associated with three-dimensional puffs in
a frame of reference moving at the bulk velocity. We establish that the flow
dynamics are relatively insensitive to the regeneration mechanisms invoked to
produce near-wall streamwise vortices and that using small, unstructured
background disturbances to regenerate the streamwise vortices is sufficient to
capture the formation of the high- and low-speed streaks and their segregation
leading to the blunting of the velocity profile characteristic of turbulent
pipe flow
A simple conceptual model of abrupt glacial climate events
Here we use a very simple conceptual model in an attempt to reduce essential
parts of the complex nonlinearity of abrupt glacial climate changes (the
so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) a
threshold process, (ii) an overshooting in the stability of the system and
(iii) a millennial-scale relaxation. By comparison with a so-called Earth
system model of intermediate complexity (CLIMBER-2), in which the events
represent oscillations between two climate states corresponding to two
fundamentally different modes of deep-water formation in the North Atlantic, we
demonstrate that the conceptual model captures fundamental aspects of the
nonlinearity of the events in that model. We use the conceptual model in order
to reproduce and reanalyse nonlinear resonance mechanisms that were already
suggested in order to explain the characteristic time scale of
Dansgaard-Oeschger events. In doing so we identify a new form of stochastic
resonance (i.e. an overshooting stochastic resonance) and provide the first
explicitly reported manifestation of ghost resonance in a geosystem, i.e. of a
mechanism which could be relevant for other systems with thresholds and with
multiple states of operation. Our work enables us to explicitly simulate
realistic probability measures of Dansgaard-Oeschger events (e.g. waiting time
distributions, which are a prerequisite for statistical analyses on the
regularity of the events by means of Monte-Carlo simulations). We thus think
that our study is an important advance in order to develop more adequate
methods to test the statistical significance and the origin of the proposed
glacial 1470-year climate cycle
Entrainment of noise-induced and limit cycle oscillators under weak noise
Theoretical models that describe oscillations in biological systems are often
either a limit cycle oscillator, where the deterministic nonlinear dynamics
gives sustained periodic oscillations, or a noise-induced oscillator, where a
fixed point is linearly stable with complex eigenvalues and addition of noise
gives oscillations around the fixed point with fluctuating amplitude. We
investigate how each class of model behaves under the external periodic
forcing, taking the well-studied van der Pol equation as an example. We find
that, when the forcing is additive, the noise-induced oscillator can show only
one-to-one entrainment to the external frequency, in contrast to the limit
cycle oscillator which is known to entrain to any ratio. When the external
forcing is multiplicative, on the other hand, the noise-induced oscillator can
show entrainment to a few ratios other than one-to-one, while the limit cycle
oscillator shows entrain to any ratio. The noise blurs the entrainment in
general, but clear entrainment regions for limit cycles can be identified as
long as the noise is not too strong.Comment: 27 pages in preprint style, 12 figues, 2 tabl
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