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This work builds on and confirms the theoretical findings of Part 1 of this paper, Moarref & Jovanovi\'c (2010). We use direct numerical simulations of the Navier-Stokes equations to assess the efficacy of blowing and suction in the form of…
We uncover activity-driven crossover from phase separation to a new turbulent state in a two-dimensional system of counter-rotating spinners. We study the statistical properties of this active-rotor turbulence using the active-rotor…
A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found.…
In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \cite{Li04}. Fluid dynamicists believe that…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…
In the recent letter Pearce et. al. Phys. Rev. Lett. 122, 168002 (2019) the authors investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal which is constrained to the surface of a torus. The underlying model…
Remarkably, even under negligible inertia, the addition of microstructural agents can generate chaotic flow fields. Such behavior can arise in polymer solutions, leading to elastic turbulence, or from active, self-driven particles, which…
We study the statistical properties of stationary, isotropic and homogeneous turbulence in two-dimensional (2D) flows, focusing on the direct cascade, that is on wave-numbers large compared to the integral scale, where both energy and…
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…
Starting from a microscopic multiparticle Langevin equation, we systematically derive a hydrodynamic description in terms of density and momentum fields for chiral active particles interacting via standard repulsive and nonlocal odd forces.…
We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal con- strained on a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural…
We investigate the Navier-Stokes turbulence driven by a stochastic random Gaussian force. Using a field-theoretic approach, we uncover an anomaly that brings hidden structure to the theory. The anomaly is generated by a non-self-adjoint…
We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed…
Turbulent flows of incompressible liquid in two dimensions are comprised of dense systems of vortices. Such system of vortices can be treated as a fluid and itself could be described in terms of hydrodynamics. We develop the hydrodynamics…
The inverse cascade in two-dimensional hydrodynamic turbulence exhibits a mysterious phenomenon. Numerical simulations have shown that the nodal isolines of certain scalars actively transported in the flow (eg, the vorticity in…
A central obstacle to understanding the route to turbulence in wall-bounded flows is that the flows are composed of complex, highly fluctuating, and strongly nonlinear states. In the case of pipe flow, models have deepened our understanding…
Turbulent flows play an important role in many aspects of nature and technics from sea storms to transport of particles or chemicals. Transport of energy from large scales to small fluctuations is the essential feature of three-dimensional…
Turbulence remains one of the central open problems in classical physics, largely due to the absence of a closed dynamical description of the Reynolds stress. Existing approaches typically rely either on local constitutive assumptions or on…
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…
Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the…