84 citations · 466 across the 37 of their papers we have counts for
38 papers
Phase transitions in the fractional three-dimensional Navier-Stokes equations
Daniel W. Boutros, John D. Gibbon
The fractional Navier-Stokes equations on a periodic domain differ from their conventional counterpart by the replacement of the Laplacian term by $ν_…
Identifying the multifractal set on which energy dissipates in a turbulent Navier-Stokes fluid
John D. Gibbon
The rich multifractal properties of fluid turbulence illustrated by the work of Parisi and Frisch are related explicitly to Leray's weak solutions of the three-dimensional Navier-S…
An analytical and computational study of the incompressible Toner-Tu Equations
John. D. Gibbon, Kolluru Venkata Kiran, Nadia Bihari Padhan +1
The incompressible Toner-Tu (ITT) partial differential equations (PDEs) are an important example of a set of active-fluid PDEs. While they share certain properties with the Navier-…
How to extract a spectrum from hydrodynamic equations
John D. Gibbon, Dario Vincenzi
Practical results gained from statistical theories of turbulence usually appear in the form of an inertial range energy spectrum and a cut-off wave-numb…
The Variable Density Model for the Rayleigh-Taylor Instability and its transformation to the diffusive, inhomogeneous, incompressible Navier-Stokes equations
John D. Gibbon
It is shown how the variable density model (VDM) that governs the Rayleigh-Taylor instability (RTI) for the miscible mixing of two incompressible fluids can be transformed into a d…
A correspondence between the multifractal model of turbulence and the Navier-Stokes equations
B. Dubrulle, J. D. Gibbon
We study a correspondence between the multifractal model of turbulence and the Navier-Stokes equations in spatial dimensions by comparing their respective dissipation length sc…