Related papers: Objective Eulerian Coherent Structures
Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has…
We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different…
We describe a large family of nonequilibrium steady states (NESS) corresponding to forced flows over obstacles. The spatial structure at large distances from the obstacle is shown to be universal, and can be quantitatively characterised in…
We describe a method for constructing $n$-orthogonal coordinate systems in constant curvature spaces. The construction proposed is a modification of Krichever's method for producing orthogonal curvilinear coordinate systems in the…
In this paper we consider the isoptic curves on the 2-dimensional geometries of constant curvature $\bE^2,~\bH^2,~\cE^2$. The topic is widely investigated in the Euclidean plane $\bE^2$ see for example \cite{CMM91} and \cite{Wi} and the…
Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
We investigate a theoretical framework for modeling fluid turbulence based on the formalism of exact coherent structures (ECSs). Although highly promising, existing evidence for the role of ECSs in turbulent flows is largely circumstantial…
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has…
We introduce a time-dependent Eulerian-Lagrangian length-scale and an inverse locality hypothesis which explain scalings of second order one-particle Lagrangian structure functions observed in Kinematic Simulations (KS) of homogeneous…
A kinematic approach for the identification of flow instabilities is proposed. By defining a flow instability in the Lagrangian frame as the increased folding of lines of fluid particles, subtle perturbations and unstable growth thereof are…
A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis…
In classical mechanics, there are two objectivities: The ``isometric objectivity'' which concerns the constitutive laws of materials once expressed in a reference frame, and the ``covariant objectivity'' which concerns the universal laws of…
It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional…
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…
Mechanical properties of tissue provide valuable information for identifying lesions. One approach to obtain quantitative estimates of elastic properties is shear wave elastography with optical coherence elastography (OCE). However, given…
In this paper, we investigate the enstrophy dynamics in relation to objective Eulerian coherent structures (OECSs) and their impact on the enstrophy and scalar transport near the turbulent/non-turbulent interface (TNTI) in flows with and…
Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We study the effect…
Optical Coherence Tomography (OCT) has become an indispensable tool for investigating mesoscopic features in soft matter and fluid mechanics. Its ability to provide high-resolution, non-invasive measurements in both spatial and temporal…
This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously…