Related papers: Mathematical Theorems on Turbulence
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence and heat transport modification in natural convection, and is one…
We propose a theoretical framework where the dissipative structures of turbulence emerge from microscopic path uncertainty. By modeling fluid parcels as stochastic tracers governed by the Schr\"odinger Bridge (SB) variational principle, we…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
Numerical models based on Reynolds-Averaged Navier-Stokes (RANS) equations are widely used in engineering turbulence modeling. However, the RANS predictions have large model-form uncertainties for many complex flows. Quantification of these…
Using the previously developed model to describe laminar/turbulent states of a viscous fluid flow, which treats the flow as a collection of coherent structures of various size (Chekmarev, Chaos, 2013, 013144), the statistical temperature of…
We show that the classical Kolmogorov and Richardson scaling laws in fully developed turbulence are consistent with a random Gaussian force field. Numerical simulations of a shell model approximation to the Navier-Stokes equations suggest…
We reexamine Liouville equation based turbulence theories proposed by Qian {[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys. A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov…
The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of…
An Eulerian-Lagrangian approach to incompressible fluids that is convenient for both analysis and physics is presented. Bounds on burning rates in combustion and heat transfer in convection are discussed, as well as results concerning…
Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of…
Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical,…
We outline our proposal for a field theory description of steady state incompressible fluid turbulence at the inertial range of scales in a general number of space dimensions. The theory consists of a Kolmogorov linear scaling mean field…
As stated in the title, the present research proposes a mathematical definition of laminar and turbulent flows, i.e., a definition that may be used to conceive and prove mathematical theorems about such flows. The definition is based on an…
The influence of turbulent effects on a fluid flow through a (pseudo) porous media is studied by numerically solving the set of Reynolds-averaged Navier-Stokes equations with the $\kappa$-$\epsilon$ model for turbulence. The spatial domains…
In this thesis, we use some methods of theory of stochastic process to approach turbulence in fluid dynamics. We discuss the Kolmogorov model for fully developed homogeneous turbulence, some recent analytical results to the 1-D Burgers'…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
The understanding of turbulent flows is one of the biggest current challenges in physics, as no first-principles theory exists to explain their observed spatio-temporal intermittency. Turbulent flows may be regarded as an intricate…
The possibility is considered that turbulence is described by differential equations for which uniqueness fails maximally, at least in some limit. The inviscid Burgers equation, in the context of Onsager's suggestion that turbulence should…
Turbulent flow has been extensively studied using computational fluid dynamics (CFD) simulations since turbulent flow regime is so frequently encountered in both academic and engineering applications. The high-fidelity simulation of the…
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…