Inertial-range transfer in two- and three-dimensional turbulence
- 14 May 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 47 (3), 525-535
- https://doi.org/10.1017/s0022112071001216
Abstract
A simple dynamical argument suggests that the k−3 enstrophy-transfer range in two-dimensional turbulence should be corrected to the form \[ E(k) = C^{\prime} \beta^{\frac{21}{3}}k^{-3}[\ln (k/k_1)]^{-\frac{1}{3}}\quad (k \gg k_1), \] where E(k) is the usual energy-spectrum function, β is the rate of enstrophy transfer per unit mass, C′ is a dimensionless constant, and k1 marks the bottom of the range, where enstrophy is pumped in. Transfer in the energy and enstrophy inertial ranges is computed according to an almost-Markovian Galilean-in variant turbulence model. Transfer in the two-dimensional energy inertial range, \[ E(k) = C\epsilon^{\frac{2}{3}}k^{-\frac{5}{3}}, \] is found to be much less local than in three dimensions, with 60 % of the transfer coming from wave-number triads where the smallest wave-number is less than one-fifth the middle wave-number. The turbulence model yields the estimates C′ = 2·626, C = 6·69 (two dimensions), C = 1·40 (three dimensions).
Keywords
This publication has 14 references indexed in Scilit:
- An almost-Markovian Galilean-invariant turbulence modelJournal of Fluid Mechanics, 1971
- Numerical Simulation of Two-Dimensional TurbulencePhysics of Fluids, 1969
- Computation of the Energy Spectrum in Homogeneous Two-Dimensional TurbulencePhysics of Fluids, 1969
- Small-Scale Structure of a Scalar Field Convected by TurbulencePhysics of Fluids, 1968
- Diffusion Approximation for Two-Dimensional TurbulencePhysics of Fluids, 1968
- Self-Consistent-Field Approach to Turbulence TheoryPhysics of Fluids, 1965
- Approximations for Steady-State Isotropic TurbulencePhysics of Fluids, 1964
- The statistical dynamics of homogeneous turbulenceJournal of Fluid Mechanics, 1964
- Turbulence spectra from a tidal channelJournal of Fluid Mechanics, 1962
- Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivityJournal of Fluid Mechanics, 1959