Related papers: Nonlinear Scale Invariance in Local Disk Flows
We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally…
We carry out three-dimensional, high resolution (up to $1024^2\times 256$) hydrodynamic simulations of the evolution of vortices in vertically unstratified Keplerian disks using the shearing sheet approximation. The transient amplification…
The linear instability of thin, vertically-isothermal Keplerian discs, under the influence of axial magnetic field is investigated. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio…
Experiments in a modified Taylor-Couette device, spanning Reynolds numbers of $10^5$ to greater than $10^6$, reveal the nonlinear stability of astrophysically-relevant flows. Nearly ideal rotation, expected in the absence of axial…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…
We relate the intermittent fluctuations of velocity gradients in turbulence to a whole range of local dissipation scales generalizing the picture of a single mean dissipation length. The statistical distribution of these local dissipation…
The variances of the fluid-particle acceleration and of the pressure-gradient and viscous force are given. The scaling parameters for these variances are velocity statistics measureable with a single-wire anemometer. For both high and low…
We consider the evolution of a family of 2D dispersive turbulence models. The members of this family involve the nonlinear advection of a dynamically active scalar field, the locality of the streamfunction-scalar relation is denoted by…
In this note we address the issue of hydrodynamical instabilities in Astrophysical rotating shear flows in the light of recent publications focused on the possibility for differential rotation to trigger and sustain turbulence in the…
We investigate properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence, by means of two direct numerical simulations of decaying turbulence with initial Mach…
Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such systems which appears…
We investigated the linear stability of pipe flow with anisotropic slip length at the wall by considering streamwise and azimuthal slip separately as the limiting cases. Our numerical analysis shows that streamwise slip renders the flow…
Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow…
Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of…
High Reynolds numbers Navier-Stokes equations are believed to break self-similarity concerning both spatial and temporal properties: correlation functions of different orders exhibit distinct decorrelation times and anomalous spatial…
The stability of a rotating fluid disk to the formation of spiral arms is studied in the tightwinding approximation in the linear regime. The dispersion relation for spirals that was derived by Bertin et al. is shown to contain a new,…
The short time evolution of three dimensional small perturbations is studied. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive hydrodynamical activity in the shape of non modal growth of initial…
For the incompressible Navier--Stokes equation, the Reynolds number ($\mathrm{Re}$) is a dimensionless parameter quantifying the relative importance of inertial over viscous forces. In the low-$\mathrm{Re}$ regime ($\mathrm{Re} \ll 1$), the…
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context of nonlinear entropy-stable discretizations, we argue that…
We use a coarse-graining approach to prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. Locality here means that interactions between disparate scales decay at least as fast as a…