Related papers: Homogeneous shear turbulence as a second-order con…
We consider two-dimensional homogeneous shear turbulence within the context of optimal control, a multi-scale turbulence model containing the fluctuation velocity and pressure correlations up to the fourth order; The model is formulated on…
We explore incompressible homogeneous isotropic turbulence within the (fourth-order model) formulation of optimal control and optimization, in contrast to the classical works of Proudman and Reid (1954) and Tatsumi (1957), with the…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
The structure of homogeneous turbulent shear flow is studied using data generated by Direct Numerical Simulations (DNS) and a linear analysis for both compressible and incompressible cases. At large values of the mean shear rate, the Rapid…
A theory of non-homogeneous turbulence is developed and is applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics and predicts power law scalings…
Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are called "exact" here. Exact equations relating 2nd and 3rd-order structure functions are obtained, as is an exact…
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed…
A wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Three-dimensional convolutional neural networks and long short-term memory are…
We discuss averaged turbulence modeling of multi-scales of length for an incompressible Newtonian fluid, with the help of the maximum information principle. We suppose that there exists a function basis to decompose the turbulent…
We use Direct Numerical Simulations (DNS) of the forced Navier-Stokes equation for a 3-dimensional incompressible fluid in order to test recent theoretical predictions. We study the two- and three-point spatio-temporal correlation functions…
Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue…
The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a…
We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic (MHD) turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation [Politano…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
This paper continues the systematic investigation of diffusive shear instabilities initiated in Part I of this series. In this work, we primarily focus on quantifying the impact of non-local mixing, which is not taken into account in Zahn's…
Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics,…
We establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems accompanied with rapidly oscillating initial data. Such result is new even for linear problems. Here we construct…
In this paper, we present theoretical results on the statistical properties of stationary, homogeneous and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the Non-Perturbative Renormalization Group,…
A statistically stationary and nearly homogeneous turbulent shear flow is established by an additional volume forcing in combination with stress-free boundary conditions in the shear direction. Both turbulent energy and enstrophy are…
The objective of this work is to investigate the utility and effectiveness of the high-order scheme for simulating unsteady turbulent flows. To achieve it, the studies were conducted from two perspectives: (i) the ability of different…