12 citations · 19 across the 8 of their papers we have counts for
8 papers
On Decay of the Local Mean Oscillations of the Vorticity Direction in Critical Navier-Stokes Flows
Zoran Grujic
We isolate and analyze the geometric PDE governing the evolution of the vorticity direction in the 3D incompressible (unforced) Navier-Stokes equations (NSE), restricted to the cas…
On higher-order derivative ratios in turbulent flows
Zoran Grujić, Muhammad Mohebujjaman
A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem…
Oscillations and integrability of the vorticity in the 3D NS flows
Y. Do, A. Farhat, Z. Grujic +1
In the studies of the Navier-Stokes (NS) regularity problem, it has become increasingly clear that a more realistic path to improved a priori bounds is to try to break away from th…
Effect of vorticity coherence on energy-enstrophy bounds for the 3D Navier-Stokes equations
Radu Dascaliuc, Zoran Grujić, Michael S. Jolly
Bounding curves in the energy,enstrophy-plane are derived for the 3D Navier-Stokes equations under an assumption on coherence of the vorticity direction. The analysis in the critic…
On energy cascades in non-homogeneous 3D Navier-Stokes equations
R. Dascaliuc, Z. Grujić
We show - in the framework of physical scales and -averages - that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale are suffic…
Vortex stretching and criticality for the 3D NSE
R. Dascaliuc, Z. Grujić
A mathematical evidence -- in a statistically significant sense -- of a geometric scenario leading to criticality of the Navier-Stokes problem is presented.
Anomalous dissipation and energy cascade in 3D inviscid flows
Radu Dascaliuc, Zoran Grujić
Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flo…
2D turbulence in physical scales of the Navier-Stokes equations
R. Dascaliuc, Z. Grujic
Local analysis of the two dimensional Navier-Stokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the si…