Effect of spatial dimension on a model of fluid turbulence

Abstract

Abstract

Critical transition to a non-chaotic regime in isotropic turbulence

“…Thus, any scaling anomalies seen in this work cannot be associated with intermittency corrections. We also note here that results from the EDQNM equation for second-and third-order statistical quantities are in good agreement with DNS measurements in three and four dimensions, as shown in Clark et al (2021b). As such, our work will focus on such quantities in determining the chaotic properties of higher-dimensional flows.…”

“…In general, these closure-based methods do not account for intermittency and thus are not suited for studies in anomalous scaling. However, they are well suited for the study of low-order statistics in higher dimensions as was carried out in Clark et al (2021b) using the EDQNM closure (Orszag 1970). Here, it was found that the enstrophy production reaches a maximum near six dimensions.…”

“…Recent studies into turbulence in dimensions higher than three (Gotoh et al 2007;Yamamoto et al 2012;Berera, Ho & Clark 2020;Clark, Ho & Berera 2021b) have shown far smaller differences when compared with three dimensions. However, some changes related to the energy cascade were observed.…”

“…Indeed, this reduction was far larger than could be expected from a central limit theorem argument. Additionally, in Clark et al (2021b), using the eddy-damped quasi-normal Markovian (EDQNM) approximation it was found that with increasing dimension the energy spectrum bottleneck effect (Falkovich 1994) is enhanced. Furthermore, it was found that the velocity derivative skewness increased until around eight dimensions before decreasing towards a potentially dimension independent constant.…”

“…Clearly, experimental flows are restricted to three dimensions, hence we must make use of numerical and analytical methods. To this end, we employ direct numerical simulation, building on our work in Berera et al (2020), and the EDQNM approximation, following on from Clark et al (2021b). As in Clark et al (2021b), where appropriate we consider comparisons between direct numerical simulation (DNS) and EDQNM results.…”