Lagrangian gradient regression for the detection of coherent structures from sparse trajectory data.

Complex flows are often characterized using the theory of Lagrangian coherent structures (LCS), which leverages the motion of flow-embedded tracers to highlight features of interest. LCS are commonly employed to study fluid mechanical systems where flow tracers are readily observed, but they are broadly applicable to dynamical systems in general. A prevailing class of LCS analyses depends on reliable computation of flow gradients.

Spectral location for the universal scaling regime in Martian atmospheric turbulence.

Atmospheric turbulence, irregular fluctuations of the fluid state, is studied on Mars. Universality of the turbulence spectrum underpins atmospheric models where computational requirements preclude full fidelity simulations of the smallest scales. However, there are discrepancies among reports on the existence and spectral location of universal scaling in Martian atmospheric data.

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization.

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modelling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate.

Computing exact coherent states in channels starting from the laminar profile: A resolvent-based approach.

We present an iterative method to compute traveling wave exact coherent states (ECS) in Couette and Poiseuille flows starting from an initial laminar profile. The approach utilizes the resolvent operator for a two-dimensional, three-component streamwise-averaged mean and exploits the underlying physics of the self-sustaining process. A singular value decomposition of the resolvent operator is used to obtain the mode shape for a single streamwise-varying Fourier mode.

Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence.

Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting modes) and resolvent analyses, i.e.

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)].