Twisting vortex lines regularize Navier-Stokes turbulence.

Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders spontaneous self-stretching and twisting of vortex lines, generating a complex hierarchy of structures. While the INSE are routinely used to describe turbulence, their regularity remains unproven; the implicit assumption being that the self-stretching is ultimately regularized by viscosity, preventing any singularities.

Saturation and Multifractality of Lagrangian and Eulerian Scaling Exponents in Three-Dimensional Turbulence.

Inertial-range scaling exponents for both Lagrangian and Eulerian structure functions are obtained from direct numerical simulations of isotropic turbulence in triply periodic domains at Taylor-scale Reynolds number up to 1300. We reaffirm that transverse Eulerian scaling exponents saturate at ≈2.1 for moment orders p≥10, significantly differing from the longitudinal exponents (which are predicted to saturate at ≈7.

Forecasting small-scale dynamics of fluid turbulence using deep neural networks.

Turbulence in fluid flows is characterized by a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small-scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality.

Scaling of Acceleration Statistics in High Reynolds Number Turbulence.

The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range. The acceleration variance at higher Reynolds numbers departs from previous predictions based on multifractal models, which characterize Lagrangian intermittency as an extension of Eulerian intermittency. The disagreement is even more prominent for higher-order moments of the acceleration.

Vorticity-Strain Rate Dynamics and the Smallest Scales of Turbulence.

Building upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events and the smallest scales of turbulence. We demonstrate that our approach is in excellent agreement with the best available data from direct numerical simulations of isotropic turbulence, with Taylor-scale Reynolds numbers up to 1300. We additionally highlight a shortcoming of prevailing intermittency models due to their disconnection from the observed correlation between vorticity and strain.

Generation of intense dissipation in high Reynolds number turbulence.

Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and pressure-Hessian-which are analysed here using direct numerical simulations of isotropic turbulence on up to [Formula: see text] grid points, and Taylor-scale Reynolds numbers in the range 140-1300. We extract the statistics involved in amplification of strain and condition them on the magnitude of strain. We find that strain is self-amplified by the quadratic nonlinearity, and depleted via vortex stretching, whereas pressure-Hessian acts to redistribute strain fluctuations towards the mean-field and hence depletes intense strain.

Turbulence is an Ineffective Mixer when Schmidt Numbers Are Large.

We solve the advection-diffusion equation for a stochastically stationary passive scalar θ, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest being 8192^{3}. The Taylor-scale Reynolds number varies in the range 140-650 and the Schmidt number Sc≡ν/D in the range 1-512, where ν is the kinematic viscosity of the fluid and D is the molecular diffusivity of θ. Our results show that turbulence becomes an ineffective mixer when Sc is large.

Small-Scale Isotropy and Ramp-Cliff Structures in Scalar Turbulence.

Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to 8192^{3} at high Péclet numbers to understand this anomaly as the scalar diffusivity, D, diminishes, or as the Schmidt number, Sc=ν/D, increases; here ν is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and Sc varies from 1 to 512.

Self-attenuation of extreme events in Navier-Stokes turbulence.

Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations. A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of Navier-Stokes equations, is non-local, i.