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We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the…
A simplified Lagrangean closure for the Navier-Stokes equation is used to study the production of intermittency in the inertial range of three dimensional turbulence. This is done using localized wavepackets following the fluid rather than…
We study the evolution of velocity fluctuations due to an isolated spatio-temporal impulse using the linearized Navier-Stokes equations. The impulse is introduced as an external body force in incompressible channel flow at $Re_\tau=10000$.…
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…
The concept of continuous topological evolution, based upon Cartan's methods of exterior differential systems, is used to develop a topological theory of non-equilibrium thermodynamics, within which there exist processes that exhibit…
Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Reynolds number, and experimentally observed properties of…
The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics (CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume…
Two-dimensional turbulence governed by the so-called $\alpha$ turbulence equations, which include the surface quasi-geostrophic equation ($\alpha=1$), the Navier--Stokes system ($\alpha=2$), and the governing equation for a shallow flow on…
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption…
Self-similar Euler singularities may be useful for understanding some aspects of Navier-Stokes turbulence. Here, a causal explanation for intermittency is given, based on the control of the sudden growth of the gradients by the Euler…
ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by…
In this study, we propose a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on the extended Navier-Stokes (N-S) equations. With some phenomenological observations and H. J. Kreuer's…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field that sustains turbulence, nonlinearity is also known to play an essential role. The goal of this study is to…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the…
We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex…
Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…
This paper extends the resolvent formulation proposed by McKeon & Sharma (2010) to consider turbulence-compliant wall interactions. Under this formulation, the turbulent velocity field is expressed as a linear superposition of propagating…
General scenario of turbulence theory is proposed and applied to streaky wall-bounded turbulence. This scenario introduces a new field of transverse waves. Significance of the theory rests on a mathematical theorem associated with the…
A rigoros analytical justification of turbulence observed in active fluids and caused by self-propulsion is presented. We prove existence of unstable wave modes for the generalized Stokes and Navier-Stokes systems by developing an approach…