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

Vortex shedding dynamics in the laminar wake of cones

Experiments on two cones of different taper ratios have been performed in the periodic Reynolds number range between 40 and 180. The visualizations of the plan view of the wake with hydrogen bubbles allow to determine local instantaneous frequencies, wavelengths and shedding angles from digital movie. The shedding frequency adjusts in a stepwise manner to the continuous variation of the cone diameter. Our results lead to revisit the original work of Gaster

WAX: A High Performance Spatial Auto-Correlation Application

We describe the algorithms employed by WAX, a spatial autocorrelation application written in C and C++ which allows for both rapid grouping of multi-epoch apparitions as well as customizable statistical analysis of generated groups. The grouping algorithm, dubbed the swiss cheese algorithm, is designed to handle diverse input databases ranging from the 2MASS working point source database (an all sky database with relatively little coverage depth) to the 2MASS working calibration source database (a database with sparse but very deep coverage). WAX retrieves apparitions and stores groups directly from and to a DBMS, generating optimized C structures and ESQL/C code based on user defined retrieval and output columns. Furthermore, WAX allows generated groups to be spatially indexed via the HTM scheme and provides fast coverage queries for points and small circular areas on the sky. Finally, WAX operates on a declination based sky subdivision, allowing multiple instances to be run simultaneously and independently, further speeding the process of merging apparitions from very large databases. The Two Micron All Sky Survey will use WAX to create merged apparition catalogs from their working point and calibration source databases, linking generated groups to sources in the already publicly available all-sky catalogs. For a given 2MASS source, this will allow astronomers to examine the properties of many related (and as yet unpublished) 2MASS extractions, and further extends the scientific value of the 2MASS data sets

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 Reλ 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 Reλ range of 50-10

Vortex shedding dynamics in the laminar wake of cones

Vortex Shedding Dynamics in the Laminar Wake of Cones Michel Provansal1 and Peter A. Monkewitz1,2 1 IRPHE Aix-Marseille Universit\'{e}s FRANCE 2LMF, EPFL, SWITZERLAND Experiments on two cones of different taper ratios have been performed in the periodic Reynolds number range between 40 and 180. The visualizations of the plan view of the wake with hydrogen bubbles allow to determine local instantaneous frequencies, wavelengths and shedding angles from digital movie. The shedding frequency adjusts in a stepwise manner to the continuous variation of the cone diameter. Our results lead to revisit the original work of Gaster

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

Reynolds number required to accurately discriminate between proposed trends of skin friction and normal stress in wall turbulence

In Nagib, Chauhan and Monkewitz~\cite{NCM07} we concluded that nearly all available $C_f$ relations for zero-pressure-gradient boundary layers are in remarkable agreement over the entire range $Re_\theta$ $<$ O($10^8$), provided one coefficient is adjusted in each relation by anchoring it to accurate measurements. Regarding the peak of the streamwise turbulence intensity $^+_P$, we conclude here that accurate measurements in flows with $Re_\tau$ $>$ O($10^6$) are required, especially when looking only at the peak $^+_P$ to discriminate between recently proposed trends. We also find remarkable agreement between the three analyses of Monkewitz \cite{M22}, Chen and Sreenivasan \cite{CS22} and Monkewitz and Nagib \cite{MN15}, with some coefficients slightly modified, by underpinning them with the same accurate measurements of $^+_P$ from reliable channel and boundary layer data. All the three analyses conclude that the inner peak of $^+$ remains finite in the limit of infinite Reynolds number, which is at variance with the unlimited growth of $^+_P$ as $\ln{Re}$ $_\tau$ predicted by the attached eddy model \cite{MM19}. Accurate measurements of high-order moments and the guidance of consistent asymptotic expansions may help clarify the issue at lower $Re_\tau$ values.Comment: 6 pages, 6 figure