63 citations · 125 across the 7 of their papers we have counts for
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Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
J. D. Gibbon, D. D. Holm
Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vorticity ($q = \bom\cdot\nablaθ$) associa…
A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations
J. D. Gibbon
Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales for weak solutions of the three-dimensional, incompressible Navier-Stoke…
Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
J. D. Gibbon, D. D. Holm
After a review of the isentropic compressible magnetohydrodynamics (ICMHD) equations, a quaternionic framework for studying the alignment dynamics of a general fluid flow is explai…
Lagrangian particle paths and ortho-normal quaternion frames
J. D. Gibbon, D. D. Holm
Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds…
Length-scale estimates for the LANS-alpha equations in terms of the Reynolds number
John D. Gibbon, Darryl D. Holm
Foias, Holm & Titi \cite{FHT2} have settled the problem of existence and uniqueness for the 3D \lans equations on periodic box . There still remains the problem, first i…
Exponentially growing solutions in homogeneous Rayleigh-Benard convection
E. Calzavarini, C. R. Doering, J. D. Gibbon +3
It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature fiel…