162 research outputs found
Intermittency and transition to chaos in the cubical lid-driven cavity flow
Transition from steady state to intermittent chaos in the cubical lid-driven
flow is investigated numerically. Fully three-dimensional stability analyses
have revealed that the flow experiences an Andronov-Poincar\'e-Hopf bifurcation
at a critical Reynolds number = 1914. As for the 2D-periodic lid-driven
cavity flows, the unstable mode originates from a centrifugal instability of
the primary vortex core. A Reynolds-Orr analysis reveals that the unstable
perturbation relies on a combination of the lift-up and anti lift-up mechanisms
to extract its energy from the base flow. Once linearly unstable, direct
numerical simulations show that the flow is driven toward a primary limit cycle
before eventually exhibiting intermittent chaotic dynamics. Though only one
eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics
during the intermittencies are surprisingly well characterized by one of the
stable eigenpairs.Comment: Accepted for publication in Fluid Dynamics Researc
Data-driven modeling of the chaotic thermal convection in an annular thermosyphon
dentifying accurate and yet interpretable low-order models from data has
gained a renewed interest over the past decade. In the present work, we
illustrate how the combined use of dimensionality reduction and sparse system
identification techniques allows us to obtain an accurate model of the chaotic
thermal convection in a two-dimensional annular thermosyphon. Taking as
guidelines the derivation of the Lorenz system, the chaotic thermal convection
dynamics simulated using a high-fidelity computational fluid dynamics solver
are first embedded into a low-dimensional space using dynamic mode
decomposition. After having reviewed the physical properties the reduced-order
model should exhibit, the latter is identified using SINDy, an increasingly
popular and flexible framework for the identification of nonlinear
continuous-time dynamical systems from data. The identified model closely
resembles the canonical Lorenz system, having a similar structure and
exhibiting the same physical properties. Finally, extensions to other flow
configurations with or without control are discussed
Time-stepping and Krylov methods for large-scale instability problems
With the ever increasing computational power available and the development of
high-performances computing, investigating the properties of realistic very
large-scale nonlinear dynamical systems has been become reachable. It must be
noted however that the memory capabilities of computers increase at a slower
rate than their computational capabilities. Consequently, the traditional
matrix-forming approaches wherein the Jacobian matrix of the system considered
is explicitly assembled become rapidly intractable. Over the past two decades,
so-called matrix-free approaches have emerged as an efficient alternative. The
aim of this chapter is thus to provide an overview of well-grounded matrix-free
methods for fixed points computations and linear stability analyses of very
large-scale nonlinear dynamical systems.Comment: To appear in "Computational Modeling of Bifurcations and
Instabilities in Fluid Mechanics", eds. A. Gelfgat, Springe
Effect of viscosity ratio on the self-sustained instabilities in planar immiscible jets
Previous studies have shown that intermediate magnitude of surface tension has a counterintuitive destabilizing effect on two-phase planar jets. In the present study, the transition process in confined two-dimensional jets of two fluids with varying viscosity ratio is investigated using direct numerical simulations (DNSs). The outer fluid coflow velocity is 17% of that of the central jet. Neutral curves for the appearance of persistent oscillations are found by recording the norm of the velocity residuals in DNS for over 1000 nondimensional time units or until the signal has reached a constant level in a logarithmic scale, either a converged steady state or a “statistically steady” oscillatory state. Oscillatory final states are found for all viscosity ratios ranging from 10−1 to 10. For uniform viscosity (m=1), the first bifurcation is through a surface-tension-driven global instability. On the other hand, for low viscosity of the outer fluid, there is a mode competition between a steady asymmetric Coanda-type attachment mode and the surface-tension-induced mode. At moderate surface tension, the first bifurcation is through the Coanda-type attachment, which eventually triggers time-dependent convective bursts. At high surface tension, the first bifurcation is through the surface-tension-dominated mode. For high viscosity of the outer fluid, persistent oscillations appear due to a strong convective instability, although it is shown that absolute instability may be possible at even higher viscosity ratios. Finally, we show that the jet is still convectively and absolutely unstable far from the inlet when the shear profile is nearly constant. Comparing this situation to a parallel Couette flow (without inflection points), we show that in both flows, a hidden interfacial mode brought out by surface tension becomes temporally and absolutely unstable in an intermediate Weber and Reynolds regime. By an energy analysis of the Couette flow case, we show that surface tension, although dissipative, can induce a velocity field near the interface that extracts energy from the flow through a viscous mechanism. This study highlights the rich dynamics of immiscible planar uniform-density jets, where different self-sustained and convective mechanisms compete and the nature of the instability depends on the exact parameter values
Numerical investigation of the interaction between laminar to turbulent transition and the wake of an airfoil
The objective of this work is to investigate numerically the different physical mechanisms of the transition to turbulence of a separated boundary-layer flow over an airfoil at low angle of attack. In this study, the spectral elements code Nek5000 is used to simulate the flow over a SD7003 wing section at an angle of attack of α = 4 ◦ . Several laminar cases are first studied from Re = 2000 to Re = 10000, and a gradual increase of the Reynolds number is then performed in order to investigate one transitional case at Re = 20000. Computations are compared with measurements where the instability mechanisms in the separated zone and near wake zone have been analyzed. The mechanism of transition is investigated, where the DMD (Dynamic Mode Decomposition) is used in order to extract the main physical modes of the flow and to highlight the interaction between the transition and the wake flow. The results suggest that the transition process appears to be physically independent of the wake flow, while the LSB shedding process is locked-in with the von Kármán instability and acts as a sub-harmonic
An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces
Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressurecorrection approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces
Deep Recurrent Encoder: A scalable end-to-end network to model brain signals
Understanding how the brain responds to sensory inputs is challenging: brain
recordings are partial, noisy, and high dimensional; they vary across sessions
and subjects and they capture highly nonlinear dynamics. These challenges have
led the community to develop a variety of preprocessing and analytical (almost
exclusively linear) methods, each designed to tackle one of these issues.
Instead, we propose to address these challenges through a specific end-to-end
deep learning architecture, trained to predict the brain responses of multiple
subjects at once. We successfully test this approach on a large cohort of
magnetoencephalography (MEG) recordings acquired during a one-hour reading
task. Our Deep Recurrent Encoding (DRE) architecture reliably predicts MEG
responses to words with a three-fold improvement over classic linear methods.
To overcome the notorious issue of interpretability of deep learning, we
describe a simple variable importance analysis. When applied to DRE, this
method recovers the expected evoked responses to word length and word
frequency. The quantitative improvement of the present deep learning approach
paves the way to better understand the nonlinear dynamics of brain activity
from large datasets
Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms
The linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of heighth and diameter d=3h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one investigated experimentally by Fransson et al. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence
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