Energy spectrum in the dissipation range

We study the dissipation range of the turbulent energy spectrum in homogeneous and isotropic turbulence via highly resolved direct numerical simulations for microscale Reynolds numbers Rλ between 1 and 100. The simulations resolve scales as small as a tenth of the Kolmogorov scale. We find that the spectrum in this range is essentially exponential for Rλ up to about 20, but assumes a more complex form for higher Rλ. This shape can be regarded roughly as a superposition of two exponentials where the second exponential, which becomes stronger with increasing Rλ, appears to be the result of intermittent interactions with the lower wave-number part of the spectrum; it disappears when these interactive parts are filtered out before computing the spectrum, essentially recovering the initial exponential shape. The multifractal theory accounts for better collapse in a limited range of wave numbers up to Reynolds numbers of 1000 observed with additional simulations at lower resolutions.