Quantifying effects of hyperviscosity on isotropic turbulence

Abstract

Isotropic hyperviscous turbulence is modelled with a pseudospectral Navier-Stokes model and comparisons are made with regular-viscosity isotropic turbulence. Two proposed means of measuring the (hyperviscous) turbulent Reynolds number are presented and critiqued, leading to a proposal for a hyperviscous turbulent Reynolds number measured as a linear function of L/λ. An analysis of the statistics of velocity and velocity-derivative fields leads to comments on appropriate uses for hyperviscosity in theoretical and practical turbulence modelling and research.

Resolving the Paradox of Oceanic Large-Scale Balance and Small-Scale Mixing

“…One can estimate that globally the small-scale dissipation is between 20% and 25% of the available energy, thus alleviating the long-standing issue in ocean and climate dynamics concerning the amount of energy dissipation. Performing modeling of such flows may mis-represent small-scale statistics, as shown for example in [32], but recent numerical experiments at moderate resolution using such a technique [33] do find an inverse cascade of energy for Boussinesq flows. The findings presented herein thus might help devise more realistic turbulence closures for the atmosphere and ocean.…”

Weak magnetohydrodynamic turbulence and intermittency

“…There is no external forcing and we fix ν 3 = 4 × 10 −15 and b 0 = 20. Note that the use of hyperviscosity might influence the intermittency properties by reducing them when the degree of hyperviscosity increases (Spyksma, Magcalas & Campbell 2012). Our analysis is systematically made at a time when the mean dissipation rate reaches its maximum, which corresponds to t * = 2196τ A with τ A = 1/(3b 0 ) (this value is taken because energy is maximum at k = 3).…”

Degeneration of internal Kelvin waves in a continuous two-layer stratification

“…The definition of the m-order hyper-viscous Reynolds number is (Lamorgese, Caughey & Pope 2005;Spyksma et al 2012)…”

“…The governing equations are the standard three-dimensional Boussinesq equations with m-order hyper-viscosity/diffusion operators (Winters & D'Asaro 1997;Waite & Bartello 2004). The use of a hyper-viscosity/diffusion approach enabled us to increase the scale separation between the forcing and dissipation length scales, producing a larger inertial subrange in the model while confining the dissipation length scales as close as possible to the grid spacing (Spyksma, Magcalas & Campbell 2012). The use of a cylindrical domain permits the derivation of the linear modal structure of IKWs for a discontinuous two-layer stratification (Csanady 1967).…”