Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows

We put forward the idea of defining vortex boundaries in planar flows as closed material barriers to the diffusive transport of vorticity. Such diffusive vortex boundaries minimize the leakage of vorticity from the fluid mass they enclose when compared to other nearby material curves. Building on recent results on passive diffusion barriers, we develop an algorithm for the automated identification of such structures from general, two-dimensional unsteady flow data. As examples, we identify vortex boundaries as vorticity diffusion barriers in two flows: an explicitly known laminar flow and a numerically generated turbulent Navier--Stokes flow.

Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows

S. Katsanoulis, M. Farazmand, M. Serra and G. Haller 

(submitted)  arXiv:1910.07355 (2019) [PDF]

Dynamic morphoskeletons in development
 

Morphogenetic flows in developmental biology are characterized by the coordinated motion of thousands of cells that organize into tissues, naturally raising the question of how this collective organization arises. Using only the kinematics of tissue deformation, which naturally integrates local and global mechanisms along cell paths, we identify the dynamic morphoskeletons behind morphogenesis, i.e., the evolving centerpieces of multi-cellular trajectory patterns. These features are model and parameter-free, frame-invariant, robust to measurement errors, and can be computed from unfiltered cell velocity data. It reveals the spatial attractors and repellers of the embryo by quantifying its Lagrangian deformation, information that is inaccessible to simple trajectory inspection or Eulerian methods that are local and typically frame-dependent. Computing these dynamic morphoskeletons in wild-type and mutant chick and fly embryos, we find that they capture the early footprint of known morphogenetic features, reveal new ones, and quantitatively distinguish between different phenotypes.

Video Credit:  C.J. Weijer Lab (Univ. of Dundee)

Dynamic morphoskeletons in development

M. Serra S. Streichan, M. Chuai, C.J. Weijer and L. Mahadevan
(submitted)  bioRxiv 657585 (2019) [PDF]

Featured to appear in SIAM NEWS 

Search and rescue at sea aided by hidden flow structures
 

Every year hundreds of people die at sea because of vessel and airplane accidents. A key challenge in reducing the number of these fatalities is to make Search and Rescue (SAR) algorithms more efficient. Here we address this challenge by uncovering hidden TRansient Attracting Profiles (TRAPs) in ocean-surface velocity data. Computable from a single velocity-field snapshot, TRAPs act as short-term attractors for all floating objects. In three different ocean field experiments, we show that TRAPs computed from measured as well as modelled velocities attract deployed drifters and manikins emulating people fallen in the water. TRAPs, which remain hidden to prior flow diagnostics, thus provide critical information for hazard responses, such as SAR and oil spill containment, and hence have the potential to save lives and limit environmental disasters.

 

 

Search and rescue at sea aided by hidden flow structures
M. Serra, P. Sathe, I. Rypina, A. Kirincich, S. Ross, P. Lermusiaux, A. Allen, T. Peacock and G. Haller 
(submitted)  arXiv:1909.07828 (2019) [PDF

MURI project with: ETH Zurich, MIT, Berkeley, VTech, WHOI, & U.S. Coast Guard

PI: Prof. T. Peacock (MIT) 

A drone-based video of the 2018 field experiment is available here

Video Credit:  VTech 

The Kinematics of Lagrangian Flow Separation in External Aerodynamics

Kinematic aspects of flow separation in external aerodynamics are investigated in the Lagrangian frame. Specifically, the initial motion of upwelling fluid material from the wall is related to the long-term attracting manifolds in the flow field. While the short-time kinematics are governed by the formation of a material spike upstream of the zero-skin-friction point and ejection of particles in direction of the asymptotic separation line, the trajectories of the fluid tracers are guided by attracting ridges in the finite-time Lyapunov exponents once they leave the vicinity of the wall. The wall signature of this initial fluid upwelling event, the so-called spiking point [Serra, M., Vetel, J., Haller, G., "Exact theory of material spike formation in flow separation", J. Fluid Mech., Vol. 845, 2018], is computed from the curvature of advected material lines and, for the first time, from high-order numerical derivatives of the wall-normal velocity obtained from direct numerical simulations of a circular cylinder and a cambered NACA 65(1)-412 airfoil. As the spline-based boundary parametrization of the airfoil profile induces oscillations, the principle spiking point can be recovered robustly through appropriate filtering. The short-term kinematics correlate strongly with the scaling lengths in the boundary layer.

Video Credit: Bjoern Klose (San Diego State University)

The Kinematics of Lagrangian Flow Separation in External Aerodynamics
B. F. Klose, M. Serra and G. B. Jacobs  
(submitted)  arXiv:1909.04129 (2019) [PDF]

Material spike formation in highly unsteady separated flows
 

We apply the frame-invariant theory of separation spike formation [Serra, M., Vetel, J., Haller, G., "Exact theory of material spike formation in flow separation", J. Fluid Mech., Vol. 845, 2018] to complex unsteady flows, including a turbulent separation bubble, an impinging jet, and flows around a freely moving cylinder and a freely rotating ellipse. We show how the theory captures the onset of material spike formation, without any assumption on the flow type (steady, periodic, unsteady) or separation type (on- or off-wall, fixed or moving boundaries). We uncover new phenomena, such as the transition from on-wall to off-wall separation, the merger of initially distinct spikes, and the presence of severe material spikes that remain hidden to previous approaches. Remarkably, even in steady flows around curved boundaries, we detect material spikes in the absence of flow reversal, the main ingredient to existing separation criteria. Together, our results unveil how an involved network of spikes arises, interacts and merges dynamically, leading to the final ejection of particles from the wall in highly transient flow separation processes.

Material spike formation in highly unsteady separated flows

M. Serra, Sean Crouzat, Gael Simon, Jérôme Vétel and George Haller

J. Fluid Mech. 883 A30 (2020) [PDF 

A Simple Variational formulation of the Incompressible Euler equations 


In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and the subsequent work on this topic rely heavily on the properties of Lie groups and Lie algebras which remain unfamiliar to most fluid dynamicists. In this note, we provide a simple derivation of Arnold's result which only uses the classical methods of calculus of variations. In particular, we show that the Lagrangian flow maps generated by the solutions of the incompressible Euler equations coincide with the stationary curves of an appropriate energy functional when the extremization is carried out over the set of volume-preserving diffeomorphisms.

Variational Lagrangian formulation of the Euler equations for incompressible flow: A simple derivation
Mohammad Farazmand and M. Serra
arXiv:1807.02726 (2018) [PDF]

Exact Theory of Material Spike Formation in Flow Separation

 

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on topological properties of material lines, our theory identifies both fixed and moving flow separation, is effective also over short-time intervals, and admits a rigorous instantaneous limit. The material backbone we identify acts as the first precursor, and the latter centerpiece, of unsteady Lagrangian flow separation.  We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified.



Exact Theory of Material Spike Formation in Flow Separation

M. Serra, Jérôme Vétel and George Haller

J. Fluid Mech. 845 (2018) 51-92. [PDF]

Efficient Computation of Null Geodesic with Applications to Coherent Vortex Detection

Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null geodesics of appropriate Lorentzian metrics defined on the flow domain. Here we derive a fully automated method for computing such null geodesics based on the geometry of geodesic flows and basic topological properties of closed planar curves.

Efficient Computation of Null Geodesics with Applications to Coherent Vortex Detection
M. Serra and George Haller
Proc. of the Royal Soc. A (2017) 473 20160807. [PDF
Featured on the journal's cover page [Link]

The polar vortices play a crucial role in the formation of the ozone hole and can cause severe weather anomalies. Their boundaries, known as the vortex ‘edges’, are typically identi- fied via methods that are either frame-dependent or return non-material structures, and hence are unsuitable for assessing material transport barriers. Using two-dimensional velocity data on isentropic surfaces in the northern hemisphere, we show that elliptic Lagrangian Coherent Structures (LCSs) identify the correct outermost material surface dividing the coherent vortex core from the surrounding incoherent surf zone. Despite the purely kinematic construction of LCSs, we find a remarkable contrast in temperature and ozone concentration across the identified vortex boundary. We also show that potential vorticity-based methods, despite their simplicity, misidentify the correct extent of the vortex edge.

Uncovering the Edge of the Polar Vortex

M. Serra, Pratik Sathe, Francisco Beron-Vera and George Haller

J. Atm. Sci. 74 (11) 3871–3885, (2017). [PDF]

Featured on Forbes - (31-01-19) [Link]

Uncovering the Edge of the Polar Vortex

Lagrangian prediction from Eulerian vortices

We propose an objective non-dimensional metric to assess the short-term persistence of Eulerian vortices identified by elliptic objective Eulerian Coherent Structures (OECSs). Elliptic OECSs, equipped with this metric, give a continuously updated picture of the coherent vortices in the flow, distinguishing them in a quantitative fashion. Our method offers a kinematical (model-independent) tool for detecting the instantaneous signature of long lived Lagrangian vortices and could forecast flow topological changes like vortex disruption and formation.

Forecasting Long-Lived Lagrangian Vortices from their Objective Eulerian Footprints
M. Serra and George Haller

J. Fluid Mech. 813 (2017) 436-457. [PDF

Objective Eulerian Coherent Structures  

We define objective Eulerian Coherent Structures (OECSs) in two-dimensional, non-autonomous dynamical systems as instantaneously most influential material curves. Specifically, OECSs are stationary curves of the averaged instantaneous material stretching-rate or material shearing-rate functionals. From these objective (frame-invariant) variational principles, we obtain explicit differential equations for hyperbolic, elliptic and parabolic OECSs. As illustration, we compute OECSs in an unsteady ocean velocity data set. In comparison to structures suggested by other common Eulerian diagnostic tools, we find OECSs to be the correct short-term cores of observed trajectory deformation patterns.


Objective Eulerian coherent structures
M. Serra
 and George Haller
Chaos, 26 (2016) 053110. [PDFEditor's pick [Link]

Hyperbolic Attracting OECSs

Parabolic  OECSs

Dependent modal space control

We propose a control logic, called Dependent Modal Space Control (DMSC), for vibration reduction in flexible structures. The well-known independent modal space control (IMSC) allows to change the frequencies and damping ratios of the controlled system, leaving the mode shapes unaltered. The DMSC, instead, allows to change also the closed loop mode shapes. We illustrate numerically and experimentally the advantages of the DMSC over the IMSC on a cantilevered beam.

Dependent modal space control: Experimental test rig
M. Serra, Francesco Ripamonti and Ferruccio Resta
J. Vibration and Control (2015): 1077546315616699. [
PDF]

 

Dependent modal space control
M. Serra, Francesco Ripamonti and Ferruccio Resta
Smart Materials and Structures 22.10 (2013): 105004. 
[PDF]