A compact exact law for compressible isothermal Hall magnetohydrodynamic turbulence

Using mixed second-order structure functions, a compact exact law is derived for isothermal compressible Hall magnetohydrodynamic turbulence with the assumptions of statistical homogeneity, time stationarity and infinite kinetic/magnetic Reynolds numbers. The resulting law is written as the sum of a Yaglom-like flux term, with an overall expression strongly reminiscent of the incompressible law, and a pure compressible source. Being mainly a function of the increments, the compact law is Galilean invariant but is dependent on the background magnetic field if one is present. Only the magnetohydrodynamic source term requires multi-spacecraft data to be estimated whereas the other components, which include those introduced by the Hall term, can be fully computed with single-spacecraft data using the Taylor hypothesis. These properties make this compact law more appropriate for analysing both numerical simulations and in situ data gathered in space plasmas, in particular when only single-spacecraft data are available.

Incipient stall characterization from skin-friction maps

Purpose The purpose of this study is the characterization of the dramatic variation in the flow scenario occurring at incipient stall conditions on a NACA0015 hydrofoil at moderate Reynolds numbers via the experimental analysis of time- and space-resolved skin-friction maps. The examined flow conditions are relevant for a variety of applications, including renewable energy production and unmanned and micro-aerial vehicles. Design/methodology/approach Grounding on the global temperature data acquired via temperature-sensitive paint, the proposed methodology adopts two approaches: one to obtain time-resolved, relative skin-friction vector fields by means of an optical-flow-based algorithm and the other one to extract quantitative, time-averaged skin-friction maps after minimization of the dissimilarity between the observed passive transport of temperature fluctuations and that suggested by the Taylor hypothesis. Findings Through the synergistic application of the proposed methods, the time-dependent evolution of the incipient stall over the hydrofoil suction side is globally described by firstly identifying the trailing edge separation at an angle of attack (AoA) AoA = 11.5°, and then by capturing the onset of upstream oriented, mushroom-like structures at AoA = 13°. The concomitant occurrence of both scenarios is found at the intermediate incidence AoA = 12.2°. Originality/value The qualitative, time-resolved skin-friction topology, combined with the quantitative, time-averaged distribution of the streamwise friction velocity, enables to establish a portrait of the complex, three-dimensional, unsteady scenario occurring at the examined flow conditions, thus providing new, fundamental information for a deeper understanding of the incipient stall development and for its control.

Stratified Inertial Subrange Inferred from In Situ Measurements in the Bottom Boundary Layer of the Rockall Channel

Deep-ocean high-resolution moored temperature data are analyzed with a focus on superbuoyant frequencies. A local Taylor hypothesis based on the horizontal velocity averaged over 2 h is used to infer horizontal wavenumber spectra of temperature variance. The inertial subrange extends over fairly low horizontal wavenumbers, typically within 2 × 10−3 and 2 × 10−1 cycles per minute (cpm). It is therefore interpreted as a stratified inertial subrange for most of this wavenumber interval, whereas in some cases the convective inertial subrange is resolved as well. Kinetic energy dissipation rate ε is inferred using theoretical expressions for the stratified inertial subrange. A wide range of values within 10−9 and 4 × 10−7 m2 s−3 is obtained for time periods either dominated by semidiurnal tides or by significant subinertial variability. A scaling for ε that depends on the potential energy within the inertio-gravity waves (IGW) frequency band PEIGW and the buoyancy frequency N is proposed for these two cases. When semidiurnal tides dominate, ε ≃ (PEIGWN)3/2, whereas ε ≃ PEIGWN in the presence of significant subinertial variability. This result is obtained for energy levels ranging from 1 to 30 times the Garrett–Munk energy level and is in contrast with classical finescale parameterization in which ε ∼ (PEIGW)2 that applies far from energy sources. The specificities of the stratified bottom boundary layer, namely a weak stratification, may account for this difference.