Asymptotics of stream-wise Reynolds stress in wall turbulence

The scaling of different features of stream-wise normal stress profiles $\langle uu\rangle^+(y^+)$ in turbulent wall-bounded flows, in particular in truly parallel flows, such as channel and pipe flows, is the subject of a long running debate. Particular points of contention are the scaling of the "inner" and "outer" peaks of $\langle uu\rangle^+$ at $y^+\approxeq 15$ and $y^+ =\mathcal{O}(10^3)$, respectively, their infinite Reynolds number limit, and the rate of logarithmic decay in the outer part of the flow. Inspired by the landmark paper of Chen and Sreenivasan (2021), two terms of the inner asymptotic expansion of $\langle uu\rangle^+$ in the small parameter $Re_\tau^{-1/4}$ are extracted for the first time from a set of direct numerical simulations (DNS) of channel flow. This inner expansion is completed by a matching outer expansion, which not only fits the same set of channel DNS within 1.5\% of the peak stress, but also provides a good match of laboratory data in pipes and the near-wall part of boundary layers, up to the highest $Re_\tau$'s of order $10^5$. The salient features of the new composite expansion are first, an inner $\langle uu\rangle^+$ peak, which saturates at 11.3 and decreases as $Re_\tau^{-1/4}$, followed by a short "wall loglaw" with a slope that becomes positive for $Re_\tau \gtrapprox 20'000$, leading up to an outer peak, and an outer logarithmic overlap with a negative slope continuously going to zero for $Re_\tau \to\infty$.Comment: 10 pages, 4 figure

Grid turbulence in dilute polymer solutions: PEO in water

Grid turbulence of polyethylene oxide (PEO) solutions (Polyox WSR-301 in ${\mathrm{H} }_{2} \mathrm{O}$ ) has been investigated experimentally for three concentrations of 25, 50 and 100 weight ppm, at a turbulence Reynolds number based on a Taylor microscale of ${\mathit{Re}}_{\lambda } \approx 100$ . For the first time, time sequences of turbulence spectra have been acquired at a rate of 0.005Hz to reveal the spectral evolution due to mechanical degradation of the polymers. In contrast to spectra averaged over the entire degradation process, the sequence of spectra reveals a clear but time-dependent Lumley scale at which the energy spectrum changes abruptly from the Kolmogorov ${\kappa }^{- 5/ 3}$ inertial range to a ${\kappa }^{- 3}$ elastic range, in which the rate of strain is maintained constant by the polymers. The scaling of the initial Lumley length with Kolmogorov dissipation rate ${\epsilon }_{0}$ and molecular weight is determined, and a cascade model for the temporal decrease of molecular weight, i.e.for the breaking of polymer chains is presented. Finally, a heuristic model spectrum is developed which covers the cases of both maximum and partial turbulence reduction by polymer

Experimental investigation into localized instabilities of mixed Rayleigh-Bénard-Poiseuille convection

The stability of the Rayleigh-Bénard-Poiseuille flow in a channel with large transverse aspect ratio (ratio of width to vertical channel height) is studied experimentally. The onset of thermal convection in the form of ‘transverse rolls' (rolls with axes perpendicular to the Poiseuille flow direction) is determined in the Reynolds-Rayleigh number plane for two different working fluids: water and mineral oil with Prandtl numbers of approximately 6.5 and 450, respectively. By analysing experimental realizations of the system impulse response it is demonstrated that the observed onset of transverse rolls corresponds to their transition from convective to absolute instability. Finally, the system response to localized patches of supercriticality (in practice local ‘hot spots') is observed and compared with analytical and numerical results of Martinand, Carrière & Monkewitz (J. Fluid Mech., vol. 502, 2004, p. 175 and vol. 551, 2006, p. 275). The experimentally observed two-dimensional saturated global modes associated with these patches appear to be of the ‘steep' variety, analogous to the one-dimensional steep nonlinear modes of Pier, Huerre & Chomaz (Physica D, vol. 148, 2001, p. 49

The hunt for the K\'arm\'an "constant'' revisited

The logarithmic law of the wall, joining the inner, near-wall mean velocity profile (MVP) to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on the value of the pre-factor, the inverse of the K\'arm\'an ``constant'' or on its universality. The choice diagnostic tool to locate logarithmic parts of the MVP is to look for regions where the indicator function $\Xi$ (equal to the wall-normal coordinate $y^+$ times the mean velocity derivative \dd U^+/\dd y^+) is constant. In pressure driven flows however, such as channel and pipe flow, $\Xi$ is significantly affected by a term proportional to the wall-normal coordinate, of order \mathcal{O}(\Reytau^{-1}) in the inner expansion, but moving up across the overlap to the leading $\mathcal{O}(1)$ in the outer expansion. Here we show, that due to this linear overlap term, \Reytau's of the order of $10^6$ and beyond are required to produce one decade of near constant $\Xi$ in channels and pipes. The problem is resolved by considering the common part of the inner asymptotic expansion carried to \mathcal{O}(\Reytau^{-1}), and the leading order of the outer expansion, which is a \textit{superposition} of log law and linear term L_0 \,y^+\Reytau^{-1}. The approach provides a new and robust method to simultaneously determine $\kappa$ and $L_0$ in pressure driven flows at currently accessible \Reytau's, and yields $\kappa$'s which are consistent with the $\kappa$'s deduced from the Reynolds number dependence of centerline velocities. A comparison with the zero-pressure-gradient turbulent boundary layer, henceforth abbreviated ``ZPG TBL'', further clarifies the issues

Grid turbulence in dilute polymer solutions: PEO in water

Grid turbulence of polyethylene oxide (PEO) solutions (Polyox WSR-301 in H2O) has been investigated experimentally for three concentrations of 25, 50 and 100 weight ppm, at a turbulence Reynolds number based on a Taylor microscale of Re-lambda approximate to 100. For the first time, time sequences of turbulence spectra have been acquired at a rate of 0.005 Hz to reveal the spectral evolution due to mechanical degradation of the polymers. In contrast to spectra averaged over the entire degradation process, the sequence of spectra reveals a clear but time-dependent Lumley scale at which the energy spectrum changes abruptly from the Kolmogorov kappa(-5/3) inertial range to a kappa(-3) elastic range, in which the rate of strain is maintained constant by the polymers. The scaling of the initial Lumley length with Kolmogorov dissipation rate epsilon(0) and molecular weight is determined, and a cascade model for the temporal decrease of molecular weight, i.e. for the breaking of polymer chains is presented. Finally, a heuristic model spectrum is developed which covers the cases of both maximum and partial turbulence reduction by polymers

A novel tethered-sphere add-on to enhance grid turbulence

The new turbulence generator consists of a standard uniform grid with tethered spheres attached to its nodes and is capable of producing approximately twice the turbulence energy per unit pressure drop coefficient C (p) than the same bare grid without the spheres. At the same time, the Reynolds number Re-lambda based on the Taylor microscale is also amplified by a factor of roughly 2, and the turbulence anisotropy is reduced to a constant level of 10% at all downstream distances without further flow conditioning after the grid. The new grid's simple design makes it suitable for a variety of fluid-flow facilities, in particular smaller water tunnels. Its performance in comparison with the plain grid is documented by measurements of the streamwise decay of turbulence energy and velocity spectra in the Re-lambda range of 50-100

Experimental investigation into localized instabilities of mixed Rayleigh-Benard-Poiseuille convection

The stability of the Rayleigh-Benard-Poiseuille flow in a channel with large transverse aspect ratio (ratio of width to vertical channel height) is studied experimentally. The onset of thermal convection in the form of 'transverse rolls' (rolls with axes perpendicular to the Poiscuille flow direction) is determined in the Reynolds-Rayleigh number plane for two different working fluids: water and mineral oil with Prandtl numbers of approximately 6.5 and 450, respectively. By analysing experimental realizations of the system Impulse response it is demonstrated that the observed onset of transverse rolls corresponds to their transition from convective to absolute instability. Finally, the system response to localized patches of supercriticality (in practice local 'hot spots') is observed and compared with analytical and numerical results of Martinand, Carriere & Monkewitz (J. Fluid Mech., vol. 502, 2004, p. 175 and vol. 551, 2006, p. 275). The experimentally observed two-dimensional saturated global modes associated with these patches appear to be of the 'steep' variety, analogous to the one-dimensional steep nonlinear modes of Pier, Huerre & Chomaz (Physica D, vol. 148, 2001, p. 49)

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie

The Zwicky Transient Facility: Science Objectives

The Zwicky Transient Facility (ZTF), a public–private enterprise, is a new time-domain survey employing a dedicated camera on the Palomar 48-inch Schmidt telescope with a 47 deg2 field of view and an 8 second readout time. It is well positioned in the development of time-domain astronomy, offering operations at 10% of the scale and style of the Large Synoptic Survey Telescope (LSST) with a single 1-m class survey telescope. The public surveys will cover the observable northern sky every three nights in g and r filters and the visible Galactic plane every night in g and r. Alerts generated by these surveys are sent in real time to brokers. A consortium of universities that provided funding (“partnership”) are undertaking several boutique surveys. The combination of these surveys producing one million alerts per night allows for exploration of transient and variable astrophysical phenomena brighter than r∼20.5 on timescales of minutes to years. We describe the primary science objectives driving ZTF, including the physics of supernovae and relativistic explosions, multi-messenger astrophysics, supernova cosmology, active galactic nuclei, and tidal disruption events, stellar variability, and solar system objects. © 2019. The Astronomical Society of the Pacific