84 citations · 466 across the 37 of their papers we have counts for
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How close are shell models to the 3D Navier-Stokes equations?
Dario Vincenzi, John D. Gibbon
Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of…
Intermittency, cascades and thin sets in three-dimensional Navier-Stokes turbulence
John D. Gibbon
Visual manifestations of intermittency in computations of three dimensional Navier-Stokes fluid turbulence appear as the low-dimensional or `thin' filamentary sets on which vortici…
Weak and strong solutions of the Navier-Stokes equations and their relation to a chessboard of convergent inverse length scales
John D. Gibbon
Using the scale invariance of the Navier-Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the Navier-Stok…
The role of BKM-type theorems in Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis
John D. Gibbon, Anupam Gupta, Nairita Pal +1
The Beale-Kato-Majda theorem contains a single criterion that controls the behaviour of solutions of the incompressible Euler equations. Versions of this theorem are discussed…
Bounds on solutions of the rotating, stratified, incompressible, non-hydrostatic, three-dimensional Boussinesq equations
John D. Gibbon, Darryl D. Holm
We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations descr…
High-low frequency slaving and regularity issues in the 3D Navier-Stokes equations
J. D. Gibbon
The old idea that an infinite dimensional dynamical system may have its high modes or frequencies slaved to low modes or frequencies is re-visited in the context of the Navier…