Related papers: Resolvent-Based Optimisation for Approximating the…
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…
By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$, and the Reynolds number $Re$ is measured using direct…
We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain,…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
The conceptual picture underlying resolvent analysis(RA) is that the nonlinear term in the Navier-Stokes(NS) equations provides an intrinsic forcing to the linear dynamics, a description inspired by control theory. The inverse of the linear…
We study Kolmogorov flow on a three dimensional, periodic domain with aspect ratios fixed to unity. Using an energy method, we give a concise proof of the linear stability of the laminar flow profile. Since turbulent motion is observed for…
We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $\Omega^*=\alpha\cos (\mathbf{p} \cdot \mathbf{x} )+\beta \sin (\mathbf{p} \cdot…
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process, and to…
If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is…
Inverse parallel schemes remain indispensable tools for computing the roots of nonlinear systems, yet their dynamical behavior can be unexpectedly rich, ranging from strong contraction to oscillatory or chaotic transients depending on the…
Plane Couette flow at Re=1200 (based on the channel half-height and half the velocity difference between the top and bottom plates) is investigated with a spatial domain designed to retain only two spanwise integral length scales. In this…
Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions,…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…
We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the L_2 norm of the resolvent of this operator…