Session 7
Thursday, 19 May 2016, 11:00 AM to 12:30 PM
20 minutes per talk, 10 minutes for questions and speaker change
From |
To |
Name |
Affiliation |
Title |
|---|---|---|---|---|
11:00am |
11:30am |
Mohammad Farazmand | Massachusetts Institute of Technology |
Polar rotation angle identifies vortices in unsteady flows |
11:30am |
12:00pm |
George Haller |
ETH Zürich |
Uncovering Lagrangian vortices objectively from the vorticity |
| 12:00pm | 12:30pm | Melissa Green | Syracuse University |
Objective detection of vortices and their evolution in 2D and 3D flows |
Session 7 Abstracts
Polar rotation angle identifies vortices in unsteady flows
Mohammad Farazmand (Massachusetts Institute of Technology)
We propose rotation inferred from the polar decomposition of the flow gradient as a diagnostic for elliptic
(or vortex-type) invariant regions in unsteady flows. We consider here two- and three-dimensional flows,
in which polar rotation can be characterized by a single angle. For this polar rotation angle (PRA), we derive
explicit formulas using the singular values and vectors of the flow gradient. We find that closed level sets
of the PRA reveal vortices in great detail, and singular level sets of the PRA uncover vortex centers.
This is joint work with George Haller.
Uncovering Lagrangian vortices objectively from the vorticity
George Haller (ETH Zürich)
Rotationally coherent Lagrangian vortices can be defined as tubes of deforming fluid elements that
complete equal bulk material rotation relative to the mean rotation of the fluid domain. Initial positions
of such tubes turn out to coincide with tubular level surfaces of the Lagrangian-Averaged Vorticity
Deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean.
LAVD- based vortices are objective and their centers are precisely the observed cyclonic attractors for
light inertial particles in oceanic flows. A similar result holds for heavy particles in anticyclonic LAVD
vortices. We illustrate the use of the LAVD to detect rotationally coherent Lagrangian vortices objectively
in several two- and three-dimensional flows.
Objective detection of vortices and their evolution in 2D and 3D flows
Melissa Green (Syracuse University)
We study the formation and shedding of vortices in two vortex-dominated flows in order to detect
coherent structures objectively (i.e., in a frame invariant fashion) in massively-separated flow. We employ
a recently developed objective definition and extraction technique for rotationally coherent Lagrangian
vortices. This methods renders material vortex boundaries as outermost convex level surfaces of the
Lagrangian-Averaged Vorticity Deviation (LAVD), i.e., the trajectory integral of the normed deviation of the
vorticity from its spatial mean. We also employ the derivative of the LAVD, the Instantaneous Vorticity
Deviation (IVD), to uncover instantaneous Eulerian vortex boundaries in an objective fashion. These
Eulerian vortex boundaries, therefore, remain the same in all possible rotating and translating unsteady
frames. The multiple methods we use identify and track both leading edge and trailing edge vortices as
they form and shed. This helps to describe the relationship between vortex dynamics and the loss of lift
during dynamic stall on a 2D flat plate undergoing a 45 degree pitch-up maneuver, and to describe the
dynamic evolution of a hairpin vortex in a three-dimensional channel flow simulation.
