Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence

Abstract

In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063(1965], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at k = k f in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k < k f , where the fluxes exhibit significant fluctuations. We show that these fluctuations arise due to the unsteady nature of the flow at small wavenumbers. For the k < k f , the shellto-shell energy transfers computed using numerical data show forward energy transfers among the neighbouring shells, but backward energy transfers for other shells.

Inverse cascade of energy in helical turbulence

“…The sum of the other triadic interactions leads to forward cascade, mainly local. The aforementioned non-local interactions leading to inverse energy cascade are also observed in two-dimensional hydrodynamic turbulence (Gupta et al 2019;Verma 2019).…”

Kolmogorov flow: Linear stability and energy transfers in a minimal low-dimensional model

“…For the stability analysis, we generate the stability matrix for S 1 and S 2 by linearizing Eqs. (27)(28)(29)(30) around S 1 , S 2 . This exercise yields a set of equations forũ 1 (k),ũ 1 (p), u 1 (q), andũ 1 (s) similar to Eqs.…”

“…The Kolmogorov flow is useful not only for analyzing transition to turbulence but also for studying the inverse cascade in two-dimensional turbulence [26][27][28] . Green 26 reported that for k > k f , kinetic energy spectrum, E(k) ∼ k −5 whereas for k < k f , E(k) ∼ k. Sommeria 17 studied the inverse cascade experimentally and reported that the exponent to be in the range of −4.5 to −4.9 for k > k f .…”

“…For k < k f , direct numerical simulations (DNS) reveal that E(k) ∼ k −5/3 . For random forcing in a wavenumber band near k = k f , Gupta et al 27 showed that for k > k f , the energy spectrum is of the form k −3 exp(−k 2 ); the exponential part gives an appearance of steeper spectrum compared to k −3 . Zhang et al 28 performed a molecular simulation using Fokker-Planck method and reported that E(k) ∼ k −4 for k < k f due to condensation in the large scale structures.…”

Hemodynamic Parameters for Cardiovascular System in 4D Flow MRI: Mathematical Definition and Clinical Applications

“…21 A vortex is a type of phenomenon observed in 2D, and the parameters related to the strength of the vortex are often discussed in 2D observation. 18,19,22 However, the swirling character of 3D flow is somewhat more complicated than vortex flow because of the helical spiral component of the flow stream in 3D. The parameter to evaluate the helical flow structure is Helicity H.…”