56 research outputs found
Surface waves enhance particle dispersion
We study the horizontal dispersion of passive tracer particles on the free
surface of gravity waves in deep water. For random linear waves with the
JONSWAP spectrum, the Lagrangian particle trajectories are computed using an
exact nonlinear model known as the John--Sclavounos equation. We show that the
single-particle dispersion exhibits an unusual super-diffusive behavior. In
particular, for large times , the variance of the tracer increases as a quadratic function of time, i.e., . This dispersion is markedly faster than Taylor's
single-particle dispersion theory which predicts that the variance of passive
tracers grows linearly with time for large . Our results imply that the wave
motion significantly enhances the dispersion of fluid particles. We show that
this super-diffusive behavior is a result of the long-term correlation of the
Lagrangian velocities of fluid parcels on the free surface
How coherent are the vortices of two-dimensional turbulence?
We use recent developments in the theory of finite-time dynamical systems to
objectively locate the material boundaries of coherent vortices in
two-dimensional Navier--Stokes turbulence. We show that these boundaries are
optimal in the sense that any closed curve in their exterior will lose
coherence under material advection. Through a detailed comparison, we find that
other available Eulerian and Lagrangian techniques significantly underestimate
the size of each coherent vortex.Comment: revised versio
Attracting and repelling Lagrangian coherent structures from a single computation
Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling
or most attracting material surfaces in a finite-time dynamical system. To
identify both types of hyperbolic LCSs at the same time instance, the standard
practice has been to compute repelling LCSs from future data and attracting
LCSs from past data. This approach tacitly assumes that coherent structures in
the flow are fundamentally recurrent, and hence gives inconsistent results for
temporally aperiodic systems. Here we resolve this inconsistency by showing how
both repelling and attracting LCSs are computable at the same time instance
from a single forward or a single backward run. These LCSs are obtained as
surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green
strain tensor.Comment: Under consideration for publication in Chaos/AI
Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Drawing upon the bursting mechanism in slow-fast systems, we propose
indicators for the prediction of such rare extreme events which do not require
a priori known slow and fast coordinates. The indicators are associated with
functionals defined in terms of Optimally Time Dependent (OTD) modes. One such
functional has the form of the largest eigenvalue of the symmetric part of the
linearized dynamics reduced to these modes. In contrast to other choices of
subspaces, the proposed modes are flow invariant and therefore a projection
onto them is dynamically meaningful. We illustrate the application of these
indicators on three examples: a prototype low-dimensional model, a body forced
turbulent fluid flow, and a unidirectional model of nonlinear water waves. We
use Bayesian statistics to quantify the predictive power of the proposed
indicators
A variational approach to probing extreme events in turbulent dynamical systems
Extreme events are ubiquitous in a wide range of dynamical systems, including
turbulent fluid flows, nonlinear waves, large scale networks and biological
systems. Here, we propose a variational framework for probing conditions that
trigger intermittent extreme events in high-dimensional nonlinear dynamical
systems. We seek the triggers as the probabilistically feasible solutions of an
appropriately constrained optimization problem, where the function to be
maximized is a system observable exhibiting intermittent extreme bursts. The
constraints are imposed to ensure the physical admissibility of the optimal
solutions, i.e., significant probability for their occurrence under the natural
flow of the dynamical system. We apply the method to a body-forced
incompressible Navier--Stokes equation, known as the Kolmogorov flow. We find
that the intermittent bursts of the energy dissipation are independent of the
external forcing and are instead caused by the spontaneous transfer of energy
from large scales to the mean flow via nonlinear triad interactions. The global
maximizer of the corresponding variational problem identifies the responsible
triad, hence providing a precursor for the occurrence of extreme dissipation
events. Specifically, monitoring the energy transfers within this triad, allows
us to develop a data-driven short-term predictor for the intermittent bursts of
energy dissipation. We assess the performance of this predictor through direct
numerical simulations.Comment: Minor revisions, generalized the constraints in Eq. (2
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