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We introduce a model for the two-dimensional Euler equations which is designed to study whether or not double exponential growth can be achieved at an interior point of the flow.

Analysis of PDEs · Mathematics 2016-01-20 Nets Hawk Katz , Andrew Tapay

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

Analysis of PDEs · Mathematics 2017-08-29 Amit Acharya , Gui-Qiang Chen , Siran Li , Marshall Slemrod , Dehua Wang

By using a formulation of motion equations for a viscous (compressible) fluid flow in terms of the vorticity and the rate of expansion as the main fluid dynamical variables, an approximation model is established for compressible flows with…

Analysis of PDEs · Mathematics 2023-08-17 Zhongmin Qian , Zihao Shen

Turbulence is one of the most fascinating phenomena in nature and one of the biggest challenges for modern physics. It is common knowledge that a flow of a simple, Newtonian fluid is likely to be turbulent, when velocity is high, viscosity…

Chaotic Dynamics · Physics 2017-05-10 Alexander Groisman , Victor Steinberg

How predictable are turbulent flows? Here we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of the solutions to the Euler equation that is…

Fluid Dynamics · Physics 2024-02-20 Dmytro Bandak , Alexei Mailybaev , Gregory L. Eyink , Nigel Goldenfeld

In this paper, we investigate Childress's conjecture proposed in [Phys.D 237(14-17):1921-1925, 2008] on the growth rate of the vorticity maximum for axisymmetric swirl-free Euler flows in three and higher dimensions. We consider the setting…

Analysis of PDEs · Mathematics 2025-11-07 Daomin Cao , Junhong Fan , Guolin Qin

The present paper is devoted to comprehensive theoretical studies of exction-polariton quantum fluids specificities in the optics of their utilization for quantum turbulence research. We show that a non-trivial implementation of…

Mesoscale and Nanoscale Physics · Physics 2025-12-01 R. Ferrini , S. V. Koniakhin

The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are…

Classical Physics · Physics 2017-08-23 Sergey L. Gavrilyuk , Henri Gouin

Prior modal stability analysis (Kojima et al., Phys. Fluids, vol. 27, 1984) predicted that a rising or sedimenting droplet in a viscous fluid is stable in the presence of surface tension no matter how small, in contrast to experimental and…

Fluid Dynamics · Physics 2015-12-01 Giacomo Gallino , Lailai Zhu , Francois Gallaire

In two dimensional turbulence, vortex thinning process is one of the attractive mechanism to explain inverse energy cascade in terms of vortex dynamics. By direct numerical simulation to the two-dimensional Navier-Stokes equations with…

Analysis of PDEs · Mathematics 2016-09-02 Tsuyoshi Yoneda

In astrophysical shear flows, the Kelvin-Helmholtz (KH) instability is generally suppressed by magnetic tension provided a sufficiently strong streamwise magnetic field. This is often used to infer upper (or lower) bounds on field strengths…

Fluid Dynamics · Physics 2026-02-04 Adrian E. Fraser , Alexis K. Kaminski , Jeffrey S. Oishi

We consider the Euler equations in ${\mathbb R}^3$ expressed in vorticity form. A classical question that goes back to Helmholtz is to describe the evolution of solutions with a high concentration around a curve. The work of Da Rios in 1906…

Analysis of PDEs · Mathematics 2020-07-16 Juan Dávila , Manuel del Pino , Monica Musso , Juncheng Wei

The non-modal transient growth of perturbations in horizontal and inclined channel flows of two immiscible fluids is studied. 3D perturbations are examined in order to find the optimal perturbations that attain the maximum amplification of…

Fluid Dynamics · Physics 2018-10-31 Ilya Barmak , Alexander Gelfgat , Amos Ullmann , Neima Brauner

We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is…

Analysis of PDEs · Mathematics 2019-10-09 Olivier Glass , Franck Sueur

The complex flow features resulting from the laminar-turbulent transition (LTT) in a sudden expansion pipe flow, with expansion ratio of 1:2 subjected to an inlet vortex perturbation is investigated by means of direct numerical simulations…

We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which…

Analysis of PDEs · Mathematics 2023-06-13 Yuchen Wang , Weicheng Zhan

We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr's initial condition…

Mathematical Physics · Physics 2009-11-11 Thomas Y. Hou , Ruo Li

This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…

Optimization and Control · Mathematics 2025-07-01 Yuta Tanabe , Kentaro Yaji , Kuniharu Ushijima

We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…

Analysis of PDEs · Mathematics 2023-01-19 Guodong Wang , Bijun Zuo

We studied turbulence induced by the Rayleigh-Taylor (RT) instability for 2D immiscible two-component flows by using a multicomponent lattice Boltzmann method with a Shan-Chen pseudopotential implemented on GPUs. We compare our results with…

Fluid Dynamics · Physics 2021-06-02 Hugo S. Tavares , Luca Biferale , Mauro Sbragaglia , Alexei A. Mailybaev