The energy spectrum of turbulence has a famous inertial range — the Kolmogorov -5/3 power law where energy cascades from large to small scales. But what happens at the smallest scales, where viscosity converts kinetic energy to heat? The dissipation range has been harder to characterize, partly because measuring it requires probes smaller than the Kolmogorov microscale.
The paper on intermediate-dissipation range energy spectra in shear turbulence (arXiv: 2603.21215) uses nanoscale hot-wire probes with sensing lengths smaller than the Kolmogorov scale to resolve the spectrum deep into the dissipation range. The experiments span Taylor-scale Reynolds numbers from 450 to 1,500 in a wind tunnel shear layer, reaching dimensionless wavenumbers up to 17 times the Kolmogorov wavenumber.
In the intermediate dissipation range — between the inertial range and the far dissipation range — the spectra collapse onto a universal form: a stretched exponential with exponent approximately 0.5, independent of Reynolds number. This is not the steep exponential cutoff assumed in simple models but a gentler, more gradual transition with a specific functional form.
The value 0.5 agrees with recent computational studies, and its Reynolds-number independence suggests genuine universality — a property of the Navier-Stokes equations themselves rather than an artifact of particular flow configurations.
The through-claim: the dissipation range is not featureless. Between the power-law inertial range and the rapid viscous cutoff lies a region with its own scaling law — a stretched exponential whose exponent is universal. The transition from inviscid cascade to viscous dissipation is not a boundary but a region, and that region has structure.
2603.21215. Turbulence / energy spectrum / dissipation range / stretched exponential / nanoscale measurements.