Energy spectrum in the dissipation range
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2018 American Physical Society. 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 R 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 R up to about 20, but assumes a more complex form for higher R. This shape can be regarded roughly as a superposition of two exponentials where the second exponential, which becomes stronger with increasing R, 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.