2,435 research outputs found
Learning the Tangent Space of Dynamical Instabilities from Data
For a large class of dynamical systems, the optimally time-dependent (OTD)
modes, a set of deformable orthonormal tangent vectors that track directions of
instabilities along any trajectory, are known to depend "pointwise" on the
state of the system on the attractor, and not on the history of the trajectory.
We leverage the power of neural networks to learn this "pointwise" mapping from
phase space to OTD space directly from data. The result of the learning process
is a cartography of directions associated with strongest instabilities in phase
space. Implications for data-driven prediction and control of dynamical
instabilities are discussed
Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
There are two main strategies for improving the projection-based reduced
order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to
the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM
bases that yield more accurate ROMs. In this paper, we use the latter. We
propose new Lagrangian inner products that we use together with Eulerian and
Lagrangian data to construct new Lagrangian ROMs. We show that the new
Lagrangian ROMs are orders of magnitude more accurate than the standard
Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to
construct the ROM basis. Specifically, for the quasi-geostrophic equations, we
show that the new Lagrangian ROMs are more accurate than the standard Eulerian
ROMs in approximating not only Lagrangian fields (e.g., the finite time
Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction).
We emphasize that the new Lagrangian ROMs do not employ any closure modeling to
model the effect of discarded modes (which is standard procedure for
low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase
in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian
inner products used to build the Lagrangian ROM basis
LOX/hydrocarbon rocket engine analytical design methodology development and validation. Volume 1: Executive summary and technical narrative
During the past three decades, an enormous amount of resources were expended in the design and development of Liquid Oxygen/Hydrocarbon and Hydrogen (LOX/HC and LOX/H2) rocket engines. A significant portion of these resources were used to develop and demonstrate the performance and combustion stability for each new engine. During these efforts, many analytical and empirical models were developed that characterize design parameters and combustion processes that influence performance and stability. Many of these models are suitable as design tools, but they have not been assembled into an industry-wide usable analytical design methodology. The objective of this program was to assemble existing performance and combustion stability models into a usable methodology capable of producing high performing and stable LOX/hydrocarbon and LOX/hydrogen propellant booster engines
Cluster-based reduced-order modelling of a mixing layer
We propose a novel cluster-based reduced-order modelling (CROM) strategy of
unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's
group (Burkardt et al. 2006) and and transition matrix models introduced in
fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a
potential alternative to POD models and generalises the Ulam-Galerkin method
classically used in dynamical systems to determine a finite-rank approximation
of the Perron-Frobenius operator. The proposed strategy processes a
time-resolved sequence of flow snapshots in two steps. First, the snapshot data
are clustered into a small number of representative states, called centroids,
in the state space. These centroids partition the state space in complementary
non-overlapping regions (centroidal Voronoi cells). Departing from the standard
algorithm, the probabilities of the clusters are determined, and the states are
sorted by analysis of the transition matrix. Secondly, the transitions between
the states are dynamically modelled using a Markov process. Physical mechanisms
are then distilled by a refined analysis of the Markov process, e.g. using
finite-time Lyapunov exponent and entropic methods. This CROM framework is
applied to the Lorenz attractor (as illustrative example), to velocity fields
of the spatially evolving incompressible mixing layer and the three-dimensional
turbulent wake of a bluff body. For these examples, CROM is shown to identify
non-trivial quasi-attractors and transition processes in an unsupervised
manner. CROM has numerous potential applications for the systematic
identification of physical mechanisms of complex dynamics, for comparison of
flow evolution models, for the identification of precursors to desirable and
undesirable events, and for flow control applications exploiting nonlinear
actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material.
Accepted for publication in Journal of Fluid Mechanic
Gravitational wave background from sub-luminous GRBs: prospects for second and third generation detectors
We assess the detection prospects of a gravitational wave background
associated with sub-luminous gamma-ray bursts (SL-GRBs). We assume that the
central engines of a significant proportion of these bursts are provided by
newly born magnetars and consider two plausible GW emission mechanisms.
Firstly, the deformation-induced triaxial GW emission from a newly born
magnetar. Secondly, the onset of a secular bar-mode instability, associated
with the long lived plateau observed in the X-ray afterglows of many gamma-ray
bursts (Corsi & Meszaros 2009a). With regards to detectability, we find that
the onset of a secular instability is the most optimistic scenario: under the
hypothesis that SL-GRBs associated with secularly unstable magnetars occur at a
rate of (48; 80)Gpc^{-3}yr^{-1} or greater, cross-correlation of data from two
Einstein Telescopes (ETs) could detect the GW background associated to this
signal with a signal-to-noise ratio of 3 or greater after 1 year of
observation. Assuming neutron star spindown results purely from triaxial GW
emissions, we find that rates of around (130;350)Gpc^{-3}yr^{-1} will be
required by ET to detect the resulting GW background. We show that a background
signal from secular instabilities could potentially mask a primordial GW
background signal in the frequency range where ET is most sen- sitive. Finally,
we show how accounting for cosmic metallicity evolution can increase the
predicted signal-to-noise ratio for background signals associated with SL-GRBs.Comment: Accepted by MNRA
Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow
Stochastic Structural Stability Theory (SSST) provides an autonomous,
deterministic, nonlinear dynamical system for evolving the statistical mean
state of a turbulent system. In this work SSST is applied to the problem of
understanding the formation of the roll/streak structures that arise from
free-stream turbulence (FST) and are associated with bypass transition in
boundary layers. Roll structures in the cross-stream/spanwise plane and
associated streamwise streaks are shown to arise as a linear instability of
interaction between the FST and the mean flow. In this interaction incoherent
Reynolds stresses arising from FST are organized by perturbation streamwise
streaks to coherently force perturbation rolls giving rise to an amplification
of the streamwise streak perturbation and through this feedback to an
instability of the combined roll/streak/turbulence complex. The dominant
turbulent perturbation structures involved in supporting the
roll/streak/turbulence complex instability are non-normal optimal perturbations
with the form of oblique waves. The cooperative linear instability giving rise
to the roll/streak structure arises at a bifurcation in the parameter of STM
excitation parameter. This structural instability eventually equilibrates
nonlinearly at finite amplitude and although the resulting statistical
equilibrium streamwise streaks are inflectional the associated flows are
stable. Formation and equilibration of the roll/streak structure by this
mechanism can be traced to the non-normality which underlies interaction
between perturbations and mean flows in modally stable systems.Comment: 16 pages, 24 figures, has been submitted for publication to Physics
of Fluid
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