Related papers: Two-point evolution equations for incompressible v…
We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable…
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…
Turbulence is an ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular,…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
In this paper, we investigate the long-time behavior of solutions to the two-dimensional Navier-Stokes equations with initial data evolving under the influence of the planar Couette flow. We focus on general perturbations, which may be…
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…
The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…
One-point time-series measurements limit the observation of three-dimensional fully developed turbulence to one dimension. For one-dimensional models, like multiplicative branching processes, this implies that the energy flux from large to…
We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…
Plasma turbulence simulations are often computationally expensive with delicate numerical stability. Yet, long simulations are needed to generate uncorrelated turbulence data for studies such as microwave scattering through density…
Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents…
As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic…
The goal of this article is to show a local exact controllability to smooth (C2) trajectories for the 2-d density dependent incompressible Navier-Stokes equations. Our controllability result requires some geometric condition on the ow of…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…
Probability density functions and conditional averages of velocity gradients derived from upper ocean observations are compared with results from forced simulations of the two-dimensional Navier-Stokes equations. Ocean data are derived from…
We present a model describing evolution of the small-scale Navier-Stokes turbulence due to its stochastic distortions by much larger turbulent scales. This study is motivated by numerical findings (laval, 2001) that such interactions of…
When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled…
Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic…
Turbulence is a non-local phenomenon and has multiple-scales. Non-locality can be addressed either implicitly or explicitly. Implicitly, by subsequent resolution of all spatio-temporal scales. However, if directly solved for the temporal or…