This content will become publicly available on June 27, 2023
 Award ID(s):
 2106233
 Publication Date:
 NSFPAR ID:
 10327734
 Journal Name:
 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
 Volume:
 380
 Issue:
 2226
 ISSN:
 1364503X
 Sponsoring Org:
 National Science Foundation
More Like this

We discuss the Onsager theory of wallbounded turbulence, analysing the momentum dissipation anomaly hypothesized by Taylor. Turbulent drag laws observed with both smooth and rough walls imply ultraviolet divergences of velocity gradients. These are eliminated by a coarsegraining operation, filtering out smallscale eddies and windowing out nearwall eddies, thus introducing two arbitrary regularization lengthscales. The regularized equations for resolved eddies correspond to the weak formulation of the Navier–Stokes equation and contain, in addition to the usual turbulent stress, also an inertial drag force modelling momentum exchange with unresolved nearwall eddies. Using an Onsagertype argument based on the principle of renormalization group invariance, we derive an upper bound on wall friction by a function of Reynolds number determined by the modulus of continuity of the velocity at the wall. Our main result is a deterministic version of Prandtl’s relation between the Blasius − 1 / 4 drag law and the 1/7 powerlaw profile of the mean streamwise velocity. At higher Reynolds, the von Kármán–Prandtl drag law requires instead a slow logarithmic approach of velocity to zero at the wall. We discuss briefly also the largeeddy simulation of wallbounded flows and use of iterative renormalization group methods to establish universal statistics inmore »

Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of highresolution and fastresponse coldwire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate ε and temperature structure function parameter C T 2 from onedimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating ε and C T 2 valid for Kolmogorov turbulence in steady state, the flux Richardson number R f and the mixing efficiency χ m are then estimated. The statistical analysis confirms the variability of R f and χ m around ~ 0.13 − 0.14 and ~ 0.16 − 0.17 , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, themore »

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A longstanding question has been whether these incipient spots already contain properties of highReynoldsnumber, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For highReynoldsnumber turbulence, such interfaces are known to display fractal scaling laws with a dimension
$D\approx 7/3$ , where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machinelearning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of$D=2.36\pm 0.03$ over almost 5 decades of spot volume, i.e., trends fully consistent with highReynoldsnumber turbulence. Additional observations pertainingmore » 
We experimentally investigate the rise velocity of finitesized bubbles in turbulence with a high energy dissipation rate of $\unicode[STIX]{x1D716}\gtrsim 0.5~\text{m}^{2}~\text{s}^{3}$ . In contrast to a 30–40 % reduction in rise velocity previously reported in weak turbulence (the Weber number ( $We$ ) is much smaller than the Eötvös number ( $Eo$ ); $We\ll 1

Dimensional analysis suggests that the dissipation length scale ( $\ell _{{\it\epsilon}}=u_{\star }^{3}/{\it\epsilon}$ ) is the appropriate scale for the shearproduction range of the secondorder streamwise structure function in neutrally stratified turbulent shear flows near solid boundaries, including smooth and roughwall boundary layers and shear layers above canopies (e.g. crops, forests and cities). These flows have two major characteristics in common: (i) a single velocity scale, i.e. the friction velocity ( $u_{\star }$ ) and (ii) the presence of large eddies that scale with an external length scale much larger than the local integral length scale. No assumptions are made about the local integral scale, which is shown to be proportional to $\ell _{{\it\epsilon}}$ for the scaling analysis to be consistent with Kolmogorov’s result for the inertial subrange. Here ${\it\epsilon}$ is the rate of dissipation of turbulent kinetic energy (TKE) that represents the rate of energy cascade in the inertial subrange. The scaling yields a loglaw dependence of the secondorder streamwise structure function on ( $r/\ell _{{\it\epsilon}}$ ), where $r$ is the streamwise spatial separation. This scaling law is confirmed by largeeddy simulation (LES) results in the roughness sublayer above a model canopy, where the imbalance between local production and dissipation of TKEmore »