English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In order to understand whether, and to what extent, spectral representationcan effectively highlight the nonlinear interaction among different scales, itis necessary to consider the state that precedes the onset of instabilities andturbulence in flows. In this condition, a system is still stable, but ishowever subject to a swarming of arbitrary 3D small perturbations. These canarrive any instant, and then undergo a transient evolution which is ruled outby the initial-value problem associated to the Navier-Stokes linearizedformulation. The set of 3D small perturbations constitutes a system of multiplespatial and temporal scales which are subject to all the processes included inthe perturbative Navier-Stokes equations: linearized convective transport,linearized vortical stretching and tilting, and the molecular diffusion.Leaving aside nonlinear interaction among the different scales, these featuresare tantamount to the features of the turbulent state. We determine theexponent of the inertial range of arbitrary longitudinal and transversalperturbations acting on a typical shear flow, i.e. the bluff-body wake. Then,we compare the present results with the exponent of the corresponding developedturbulent state (notoriously equal to -5/3). For longitudinal perturbations, weobserve a decay rate of -3 in the inertial range, typically met intwo-dimensional turbulence. For purely 3D perturbations, instead, the energydecreases with a factor of -5/3. If we consider a combination of longitudinaland transversal perturbative waves, the energy spectrum seems to have a decayof -3 for larger wavenumbers ([50, 100]), while for smaller wavenumbers([3,50]) the decay is of the order -5/3. We can conclude that the value of theexponent of the inertial range has a much higher level of universality, whichis not necessarily associated to the nonlinear interaction.

Pre-unstable set of multiple transient three-dimensional perturbation waves and the associated turbulent state in a shear flow