Three-dimensional turbulence without vortex stretching

Self Cite

We consider the relaxation to thermal equilibrium of the Galerkin-truncated Euler equations in three dimensions, from which vortex stretching is removed. We prove that helicity and enstrophy are conserved by the system. Using statistical mechanics, we derive analytical predictions for the equilibrium energy and helicity spectra. Results are verified using pseudo-spectral direct numerical simulations. Results show that if the initial condition contains helicity, the system relaxes to a force-free large-scale structure akin to an Arnold–Beltrami–Childress (ABC) flow.

Section: Introductionmentioning

confidence: 91%

Section: Conservation Of Integral Quantitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…with ω = ∇ × u and u the velocity. Previously (Bos 2021), we used closure analysis to reveal that turbulence without vortex stretching, which conserves enstrophy defined as…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Statistical mechanics of the Euler equations without vortex stretching

Bos²

2021

Self Cite

Critical transition to a non-chaotic regime in isotropic turbulence

Clark

Armua

et al. 2021

We study the properties of homogeneous and isotropic turbulence in higher spatial dimensions through the lens of chaos and predictability using numerical simulations. We employ both direct numerical simulations and numerical calculations of the eddy damped quasi-normal Markovian closure approximation. Our closure results show a remarkable transition to a non-chaotic regime above the critical dimension, $d_c$ , which is found to be approximately 5.88. We relate these results to the properties of the energy cascade as a function of spatial dimension in the context of the idea of a critical dimension for turbulence where Kolmogorov's 1941 theory becomes exact.

Nonlinear amplification in hydrodynamic turbulence

Iyer

Sreenivasan

Yeung³

2021

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.