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Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however; they can cause significant…
We derive the scale-by-scale uncertainty energy budget equation and demonstrate theoretically and computationally the presence of a self-similar equilibrium cascade of decorrelation in an inertial range of scales during the time range of…
The quasi-periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible Navier-Stokes flow on a three-periodic domain. Special symmetries are imposed on the flow…
Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…
We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or…
For the steady-state direct cascade of two-dimensional Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. The probability density function (pdf) of the vorticity coarse-grained over a scale in…
We investigate how the rotational nature of turbulence affects learned mappings between quantities governed by the Navier-Stokes equations. By varying the degree of anisotropy in a turbulence dataset, we explore how statistical symmetry…
The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent…
We consider linear feedback flow control of the largest scales in an incompressible turbulent channel flow at a friction Reynolds number of Re$_{\tau}$ = 2000. A linear model is formed by linearizing the Navier-Stokes equations about the…
The statistical properties of interstellar turbulence are studied by means of three-dimensional high-resolution HD and MHD simulations of a SN-driven ISM. It is found that the longitudinal and transverse turbulent length scales have time…
Recently, Liao and Qin [J. Fluid Mech. 1008, R2 (2025)] claimed that numerical noise in direct numerical simulation of turbulence using the deterministic Navier-Stokes equations is "approximately equivalent" to the physical noise arising…
We inquire the statistical properties of the pair formed by the Navier-Stokes equation for an incompressible velocity field and the advection-diffusion equation for a scalar field transported in the same flow in two dimensions (2d). The…
Anomalous scaling problem in the stochastic Navier-Stokes equation is treated in the framework of the field theoretical approach, successfully applied earlier to the Kraichnan rapid advection model. Two cases of the space dimensions d=2 and…
Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We…
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
We propose and verify a wave-vector-space version of generalized extended self similarity and broaden its applicability to uncover intriguing, universal scaling in the far dissipation range by computing high-order ($\leq 20\/$) structure…
Series of lectures on statistical turbulence written for amateurs but not experts. Elementary aspects and problems of turbulence in two and three dimensional Navier-Stokes equation are introduced. A few properties of scalar turbulence and…
Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often…
Numerical calculations of Helium-II hydrodynamics show that a dense tangle of superfluid vortices induces in an initially stationary normal fluid a highly dissipative, complex, vortical flow pattern ("turbulence") with a -2.2 energy…
We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse…