60 citations · 730 across the 55 of their papers we have counts for
59 papers
Distance Geometry and a Hydrodynamical Hopf-Rinow Criterion
Theodore D. Drivas, Patrick Heslin, Gerard Misiołek
The hydrodynamical Hopf-Rinow problem asks whether a given reconfiguration of an ideal fluid can be attained by an Euler flow. On the flat two-dimensional torus, we give an equival…
Geometry of strong forces in continuum mechanics
Theodore D. Drivas, Daniil Glukhovskiy
Consider a material point in finite dimensions moving under the influence of a potential force according to Newton's laws. Suppose the potential energy function is a generalized we…
On the collapse of three point vortices on surfaces
Theodore D. Drivas, Boris A. Khanikati, Valeriya A. Khanikati
Point vortices represent an important reduced model describing two-dimensional ideal fluid dynamics. It is well known that there exist three-vortex configurations on the Euclidean…
Mathematical Theorems on Turbulence
Theodore D. Drivas
In these notes, we emphasize Theorems rather than Theories concerning turbulent fluid motion. Such theorems can be viewed as constraints on the theoretical predictions and expectat…
On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
Theodore D. Drivas, Tarek M. Elgindi, Daniel Ginsberg
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in…
Lagrangian aspects of Yudovich theory for 2D Euler
Theodore D. Drivas, Joonhyun La
In this note, we establish Yudovich's existence and uniqueness result for bounded (as well as mildly unbounded) vorticity weak solution of the two-dimensional incompressible Euler…
Anomalous dissipation and regularization in isotropic Gaussian turbulence
Theodore D. Drivas, Lucio Galeati, Umberto Pappalettera
In this work we rigorously establish a number of properties of "turbulent" solutions to the stochastic transport and the stochastic continuity equations constructed by Le Jan and R…
How doth the random triangle
Theodore D. Drivas, Michael Retakh
Charles L. Dodgson, also known as Lewis Carroll, in his book "Pillow problems" from 1893 asked for the likelihood of a random triangle to be obtuse. Clearly, the answer to Dodgson'…
On the fragility of laminar flow
Theodore D. Drivas, Daniel Ginsberg, Marc Nualart
Inviscid laminar flow is a stationary solution of the incompressible Euler equations whose streamlines foliate the fluid domain. Their structure on symmetric domains is rigid: all…
Whither the Zeroth Law of Turbulence?
Kartik P. Iyer, Theodore D. Drivas, Gregory L. Eyink +1
Experimental and numerical studies of incompressible turbulence suggest that the mean dissipation rate of kinetic energy remains constant as the Reynolds number tends to infinity (…
Intermittency and Dissipation Regularity in Turbulence
Luigi De Rosa, Theodore D. Drivas, Marco Inversi +1
We lay down a geometric-analytic framework to capture properties of energy dissipation within weak solutions to the incompressible Euler equations. For solutions with spatial Besov…
A geometric characterization of steady laminar flow
Theodore D. Drivas, Marc Nualart
We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non-contractible streamlines which…
Pensive billiards, point vortices, and the silver ratio
Theodore D. Drivas, Daniil Glukhovskiy, Boris Khesin
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before…
Singular vortex pairs follow magnetic geodesics
Theodore D. Drivas, Daniil Glukhovskiy, Boris Khesin
We consider pairs of point vortices having circulations and and confined to a two-dimensional surface . In the limit of zero initial separation , we pro…
Statistically self-similar mixing by Gaussian random fields
Michele Coti Zelati, Theodore D. Drivas, Rishabh S. Gvalani
We study the passive transport of a scalar field by a spatially smooth but white-in-time incompressible Gaussian random velocity field on . If the velocity field …
The Feynman-Lagerstrom criterion for boundary layers
Theodore D. Drivas, Sameer Iyer, Trinh T. Nguyen
We study the boundary layer theory for slightly viscous stationary flows forced by an imposed slip velocity at the boundary. According to the theory of Prandtl (1904) and Batchelor…
On the large-scale sweeping of small-scale eddies in turbulence -- A filtering approach
Theodore D. Drivas, Perry L. Johnson, Cristian C. Lalescu +1
We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the a…
Islands in stable fluid equilibria
Theodore D. Drivas, Daniel Ginsberg
We prove that stable fluid equilibria with trivial homology on curved, reflection-symmetric periodic channels must posses "islands", or cat's eye vortices. In this way, arbitrarily…
Twisting in Hamiltonian Flows and Perfect Fluids
Theodore D. Drivas, Tarek M. Elgindi, In-Jee Jeong
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting…
On the Support of Anomalous Dissipation Measures
Luigi De Rosa, Theodore D. Drivas, Marco Inversi
By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solut…
On the distribution of heat in fibered magnetic fields
Theodore D. Drivas, Daniel Ginsberg, Hezekiah Grayer
We study the equilibrium temperature distribution in a model for strongly magnetized plasmas in dimension two and higher. Provided the magnetic field is sufficiently structured (in…
On maximally mixed equilibria of two-dimensional perfect fluids
Michele Dolce, Theodore D. Drivas
The vorticity of a two-dimensional perfect (incompressible and inviscid) fluid is transported by its area preserving flow. Given an initial vorticity distribution , predicting…
Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids
Theodore D. Drivas, Tarek M. Elgindi, Joonhyun La
We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure o…
Singularity formation in the incompressible Euler equation in finite and infinite time
Theodore D. Drivas, Tarek M. Elgindi
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattere…