Results of direct numerical simulations (DNS) of porous-wall turbulent flows in open channels with conjugate heat transfer are reported in this work. For the conductive porous walls considered here, the change in heat transfer is not monotonic. The heat flux initially decreases when going from a conductive smooth wall to slightly porous walls. In this initial porous-wall turbulence regime, the near-wall flow remains smooth-wall like and the heat transfer is dominated by molecular diffusion. As such, a reduction of the more favorably conducting solid material diminishes the overall heat transfer performance. Beyond a certain level of permeability however, the near-wall flow transitions to the K-H-like regime marked by the presence of cross-stream rollers, and the heat flux undergoes an increasing trend until it eventually surpasses that of smooth-wall turbulence. Neglecting the thermal behavior of the solid material can therefore result in overestimation of any gains in heat transfer. Additionally, thermal performance is assessed in terms of the Reynolds analogy breakdown, which is the disparity between the fractional increases in the Stanton number, St, and the fractional increases in the skin-friction coefficient, C_f, relative to smooth-wall flow. Similar to rough walls, the breakdown is unfavorable for porous walls. The unfavorable breakdown in Reynolds analogy is due to growing dissimilarities between the transfer of momentum and heat in the vicinity of the porous wall as it becomes more permeable. Turbulent sweep and ejection type events contribute more significantly to momentum transfer across the permeable surface than they do to heat transfer. However, unlike for rough walls, a saturation limit for heat transfer is not observed for the porous walls considered here. How much of a maximum increase in heat transfer can be achieved is something that remains to be determined.

We study the stability of plane Poiseuille flow (PPF) and plane Couette flow (PCF) subject to streamwise system rotation using linear stability analysis and direct numerical simulations. The linear stability analysis reveals two asymptotic regimes depending on the non-dimensional rotation rate ( $\textit{Ro}$ ): a low- $\textit{Ro}$ and a high- $\textit{Ro}$ regime. In the low- $\textit{Ro}$ regime, the critical Reynolds number $\textit{Re}_c$ and critical streamwise wavenumber $\alpha _c$ are proportional to $\textit{Ro}$ , while the critical spanwise wavenumber $\beta _c$ is constant. In the high- $\textit{Ro}$ regime, as $\textit{Ro} \rightarrow \infty$ , we find $\textit{Re}_c = 66.45$ and $\beta _c = 2.459$ for streamwise-rotating PPF, and $\textit{Re}_c = 20.66$ and $\beta _c = 1.558$ for streamwise-rotating PCF, with $\alpha _c\propto 1/Ro$ . Our results for streamwise-rotating PPF match previous findings by Masuda et al. (J. Fluid Mech., vol. 603, 2008, pp. 189-206). Interestingly, the critical values of $\beta _c$ and $\textit{Re}_c$ at $\textit{Ro} \rightarrow \infty$ in streamwise-rotating PPF and PCF coincide with the minimum $\textit{Re}_c$ reported by Lezius & Johnston (J. Fluid Mech., vol. 77, 1976, pp. 153-176) and Wall & Nagata (J. Fluid Mech., vol. 564, 2006, pp. 25-55) for spanwise-rotating PPF at $\textit{Ro}=0.3366$ and PCF at $\textit{Ro}=0.5$ . We explain this similarity through an analysis of the perturbation equations. Consequently, the linear stability of streamwise-rotating PCF at large $\textit{Ro}$ is closely related to that of spanwise-rotating PCF and Rayleigh-B & eacute;nard convection, with $\textit{Re}_c = \sqrt {Ra_c}/2$ , where $Ra_c$ is the critical Rayleigh number. To explore the potential for subcritical transitions, direct numerical simulations were performed. At low $\textit{Ro}$ , a subcritical transition regime emerges, characterised by large-scale turbulent-laminar patterns in streamwise-rotating PPF and PCF. However, at higher $\textit{Ro}$ , subcritical transitions do not occur and the flow relaminarises for $\textit{Re} \lt Re_c$ . Furthermore, we identify a narrow $\textit{Ro}$ range where turbulent-laminar patterns develop under supercritical conditions.

Rotation influences flows and transport processes in many engineering applications, however, even in canonical flow cases, the effects of rotation are not fully understood. Here, we present the results of di-rect numerical simulations of heat transfer plane Couette and Taylor-Couette flows subject to rotation about the spanwise and axial axis, respectively. Temperature is a passive scalar since buoyancy is ne-glected. The Reynolds number Re and the rotation rate Rn are systematically varied to thoroughly inves-tigate the influence of rotation on heat and momentum transfer and the Reynolds analogy. We find that with increasing anti-cyclonic rotation, the Nusselt numbers for the momentum transfer Num and heat transfer Nuh both increase at first before declining and approaching unity at rapid rotation rates when the flow becomes fully laminar. The Reynolds analogy factor RA = N uh/N um is near unity for non-rotating Couette flows, but it grows significantly with increasing rotation rate. RA reaches a maximum of approx-imately 2 at low Re up to 6 and 8 near Rn = 1 at higher Re in plane Couette and Taylor-Couette flow, respectively. The simulations thus show that the Reynolds analogy between heat and momentum trans-fer breaks down and that the heat transfer can become much faster than moment transfer when plane Couette and Taylor-Couette flows are subject to anti-cyclonic rotation. This happens at low Re as well as higher Re when the flows are fully turbulent. The turbulent Prandtl becomes much smaller than unity and the mean velocity and temperature profiles differ when the Reynolds analogy breaks down. We also present empirical models for Num and RA , which agree reasonably well to very well with the data within a limited Rn range.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Complementing large-eddy simulation (LES) with wall-modelling is, perhaps, the most straight-forward way to enable high-fidelity simulations at high Reynolds numbers. At the same time, high-order methods offer the benefits of high computational efficiency and potentially faster convergence with respect to mesh refinement even outside the asymptotic regime.

A recently developed so-called explicit algebraic Reynolds-stress (EARS) model is applied to a transitioning atmospheric boundary layer (ABL). The simulation describes a diurnal cycle with a deep convective ABL during daytime and an extremely thin and stably stratified ABL during nighttime. The predictions of the EARS model are compared to large-eddy simulations (LES) of Couvreux et al. (Bound Layer Meteorol 176:369-400, 2020). The model simulation is extended in time in order to study several consecutive diurnal cycles. The EARS model uses the same parametrization and model coefficients for stable and convective ABL and is applicable over a wide range of thermal stratifications. First-order statistics are shown to be well predicted by the model. We also show that the model can predict transitional effects such as residual turbulence as well as horizontal turbulent fluxes, which are an inherent part of the EARS model solution.

Heat and mass transport are generally closely correlated to momentum transport in shear flows. This so-called Reynolds analogy between advective heat or mass transport and momentum transport hinders efficiency improvements in engineering heat and mass transfer applications. I show through direct numerical simulations that in plane Couette and Taylor-Couette flow, rotation can strongly influence wall-to-wall passive tracer transport and make it much faster than momentum transport, clearly in violation of the Reynolds analogy. This difference between passive tracer transport, representative of heat/mass transport, and momentum transport is observed in steady flows with large counter-rotating vortices at low Reynolds numbers as well as in fully turbulent flows at higher Reynolds numbers. It is especially large near the neutral (Rayleigh's) stability limit. The rotation-induced Coriolis force strongly damps the streamwise/azimuthal velocity fluctuations when this limit is approached, while tracer fluctuations are much less affected. Accordingly, momentum transport is much more reduced than tracer transport, showing that the Coriolis force breaks the Reynolds analogy. At higher Reynolds numbers, this strong advective transport dissimilarity is accompanied by approximate limit cycle dynamics with intense low-frequency bursts of turbulence when approaching the neutral stability limit. The study demonstrates that simple body forces can cause clear dissimilarities between heat/mass and momentum transport in shear flows.

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$ , resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$ . A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

A recently developed explicit algebraic Reynolds-stress (EARS) model is validated for an idealized representation of the night-time high-latitude stably stratified atmospheric boundary layer. The simulations are made with four surface cooling rates that result in weakly to moderately stratified stable boundary layers. The predictions of the EARS model are compared to high-resolution large-eddy simulations (LES) of Sullivan et al. (J Atmos Sci 73(4):1815-1840, 2016). First- and second-order statistics are shown to be well predicted by the EARS model. The EARS model also predicts the horizontal turbulent fluxes and turbulence anisotropy and these compare well with the LES results. The sensitivity to the model coefficients is studied by comparing the EARS model results with LES results. Finally, we propose a new scaling for the production of turbulence kinetic energy and show that the EARS model captures the essential trends of the LES results for different cooling rates.

The displacement speed that characterises the self-propagation of isosurfaces of a reaction progress variable is of key importance for turbulent premixed reacting flow. The evolution equation for the displacement speed was derived in a recent work of Yu and Lipatnikov (Phys Rev E 100:013107, 2019a) for the case where the flame is described by a transport equation for single reaction progress variable assuming simple transport and one-step chemistry. This equation represents interaction of a number of complex coupled mechanisms related to straining by the velocity field, surface curvature and the scalar gradient. The aim of the current work is to provide detailed physical explanations of the displacement speed equation and its various terms, and to provide a new perspective to understand the mechanisms responsible for observed variations in the displacement speed. The equation is then used to analyze the propagation of a statistically planar reaction wave in homogeneous isotropic constant-density turbulence using direct numerical simulations. Additional emphasis is put on retracting surface segments that have a negative displacement speed, a phenomenon that commonly occurs at high Karlovitz numbers.

This repository contains data that was used for publishing article called Modelling of Stably Stratified Atmospheric Boundary Layers with Varying Stratifications. The repository compliments the publication in the sense that it provides qualitative insight for comparison and exploration. Keywords: GABLS1, Open data, Stably-stratified turbulence, Turbulence parametrization The data is stored inside sixteen files. The file names are split into a part that describes variables and part that describes simulation. Here's an example of a file name: budgets.cr0375.csv The first part budgets refers to variables inside the file and the second part cr0375 refers to forcing conditions (in this example cooling rate of 0.375 Kelvin per hour) used in the simulation. Variables: mean wind speed and mean potential temperature (first_order_stat) variance and covariance variables that describe turbulence properties (second_order_stat) variables in the turbulent kinetic energy and half the temperature variance equations (budgets) contain values for model coefficients that can be used for calculating second order statistics (lambda_beta_coeffs) Simulations: cooling rate at the surface 0.25 Kelvin per hour (cr025) cooling rate at the surface 0.375 Kelvin per hour (cr0375) cooling rate at the surface 0.5 Kelvin per hour (cr05) cooling rate at the surface 1.0 Kelvin per hour (cr1) Note: The results presented in the repository are taken after the ninth hour of the simulation while the results in the published paper is averaged between the eight and ninth hour. This difference should be negligible.

DNS have been performed of turbulent channel flow with spanwise rotation and bulk Reynolds number Re up to 30000. At moderate rotation rates Ro the flow on one side of the channel is approximately ...

In a recent study (Želi et al. in Bound Layer Meteorol 176:229–249, 2020), we have shown that the explicit algebraic Reynolds-stress (EARS) model, implemented in a single-column context, is able to capture the main features of a stable atmospheric boundary layer (ABL) for a range of stratification levels. We here extend the previous study and show that the same formulation and calibration of the EARS model also can be applied to a dry convective ABL. Five different simulations with moderate convective intensities are studied by prescribing surface heat flux and geostrophic forcing. The results of the EARS model are compared to large-eddy simulations of Salesky and Anderson (J Fluid Mech 856:135–168, 2018). It is shown that the EARS model performs well and is able to capture the counter-gradient heat flux in the upper part of the ABL due to the presence of the non-gradient term in the relation for vertical turbulent heat flux. The model predicts the full Reynolds-stress tensor and heat-flux vector and allows us to compare other important aspects of a convective ABL such as the profiles of vertical momentum variance. Together with the previous studies, we show that the EARS model is able to predict the essential features of the ABL. It also shows that the EARS model with the same model formulation and coefficients is applicable over a wide range of stable and moderately unstable stratifications.

There is a rapidly growing interest in using general-purpose CFD codes based on second-order finite volume methods for Large-Eddy Simulation (LES) in a wide range of applications, and in many cases involving wall-bounded flows. However, such codes are strongly affected by numerical dissipation and the accuracy obtained for typical LES resolutions is often poor. In the present study, we approach the problem of improving the LES capability of such codes by reduction of the numerical dissipation and use of an anisotropy-capturing subgrid-scale (SGS) stress model. The latter is of special importance for wall-resolved LES with resolutions where the SGS anisotropy can be substantial. Here we use the Explicit Algebraic (EA) SGS model [Marstorp L, Brethouwer G, Grundestam O, et al. Explicit algebraic subgrid stress models with application to rotating channel flow. J Fluid Mech. 2009;639:403-432], and comparisons are made for channel flow at friction Reynolds numbers up to 934 with the dynamic Smagorinsky model. The numerical dissipation is reduced by using an OpenFOAM based custom-built flow solver that modifies the Rhie and Chow interpolation and allows to control and minimise its effects without causing numerical instability (in viscous, fully turbulent flows). Different resolutions were used and large improvements of the LES accuracy were demonstrated for skin friction, mean velocity and other flow statistics by use of the new solver in combination with the EA SGS model. By reducing the numerical dissipation and using the EA SGS model the resolution requirements for wall-resolved LES can be significantly reduced.

Periodic hill channel flow at two different bulk Reynolds numbers of 10595 and 37000 is studied by wall-resolved large-eddy simulations (LES) to investigate the detailed Reynolds number effects of ...

Concerning wall resolved large-eddy simulation (LES), a considerable reduction of computational resources is achievable by employing the Explicit Algebraic subgrid scale model (EAM) (\cite{marstorp ...

Direct numerical simulations of passive scalar transport in turbulent channel flow subject to spanwise rotation are carried out with two different boundary conditions for the scalar. In the first case the scalar transport is driven by an assigned scalar difference at the walls and in the second case by a constant mean streamwise scalar gradient. The Reynolds number Re = U(b)h/nu is fixed at 14 000 and the rotation number Ro = 2 Omega h/U-b is varied from 0 to 0.75, where U-b is the mean bulk velocity, h half the channel gap width, and Omega the rotation rate. This work is a continuation of Brethouwer [J. Fluid Mech. 844, 297 ( 2018)] to further study the influence of rotation and also the influence of scalar boundary conditions on scalar transport in channel flow. Mean scalar profiles and other scalar statistics differ in the two cases with different boundary conditions but are similar in the near-wall region in terms of local wall units. The conclusion of Brethouwer that the Reynolds analogy for scalar-momentum transfer does not apply to rotating channel flow is independent of scalar boundary conditions. Rotation influences the turbulent scalar flux differently than the Reynolds shear stress and strongly reduces the turbulent Prandtl number on the unstable channel side, irrespective of the scalar boundary conditions. Scalar structures are larger than the turbulence structures in rotating channel flow, in contrast to nonrotating channel flow where these are similar.

It is well known that the spanwise rotation in turbulent channel flow alters the mean velocity distribution to a linear law. In the present work, we have studied the higher-order moments of the streamwise fluctuations in a turbulent channel flow with spanwise rotation. Our results show that in a significant part of the channel the 2p-order moments, raised by the power 1/p with p = 1,2, ... ,6, also follow linear behavior according to <(u'(+))(2p)>(1/p) = a(p) (y/h) + b(p). Here, u'(+) is the streamwise velocity fluctuation normalized by the global friction velocity, h is the channel half width, and b(p) and a(p) are the intercept and the slope, respectively, which vary with Reynolds and rotation numbers. The linear regions can be extended by introducing a self-similar scaling, that is, 2p-order moments as a function of 2q-order moments. The slopes in the self-similar scaling a(p)/a(1) do not reveal sub-Gaussian behavior as in nonrotating wall-bounded flows, but rather Gaussian or super-Gaussian behaviors.

In most subcritical planar shear flows, the transitional regime features oblique large-scale laminar-turbulent patterns. So far, such laminar-turbulent patterns have only been investigated in flows over perfectly smooth walls and little attention has been devoted to cases with rough surfaces as found in most practical engineering, urban applications, and in nature. In this study, we investigate laminar-turbulent patterns in plane Couette flow with one rough wall by means of direct numerical simulation, as a function of the Reynolds number and of the roughness height. The roughness is modeled using a force term in the Navier–Stokes equations. The focus of this study is on a new regime featuring non-oblique turbulent bands transverse to the motion of the walls, and separated by arbitrary long laminar gaps. This regime is found when the wall is sufficiently rough. This transverse turbulent band occurs at Reynolds numbers just below the onset of self-sustained turbulence found in the smooth wall case. The localized turbulence patches have a streamwise extent as large as 50–180 gap widths, decreasing with decreasing Reynolds number. The turbulent fraction as well as the band width show a linear relationship with the Reynolds number.

Standard turbulence models for the atmospheric boundary layer (ABL) typically use boundary conditions based on the Monin–Obukhov similarity theory (MOST). This can lead to inconsistency between the boundary condition and the closure model. Here, we propose a new boundary-condition treatment of the stratified ABL, derived for the so-called explicit algebraic Reynolds-stress model. The boundary conditions correspond to the relations for vanishing buoyancy effects that are valid close to the ground. The solution for the stratified surface layer is in agreement with the surface scaling physics and MOST functions. This was validated in a simulation of an idealized diurnal cycle of the ABL based on the second Global Energy and Water cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS2) case.

Passive scalar transport in turbulent channel flow subject to spanwise system rotation is studied by direct numerical simulations. The Reynolds number $Re=U_{b}h/\unicode[STIX]{x1D708}$ is fixed at 20 000 and the rotation number $Ro=2\unicode[STIX]{x1D6FA}h/U_{b}$ is varied from 0 to 1.2, where $U_{b}$ is the bulk mean velocity, $h$ the half channel gap width and $\unicode[STIX]{x1D6FA}$ the rotation rate. The scalar is constant but different at the two walls, leading to steady scalar transport across the channel. The rotation causes an unstable channel side with relatively strong turbulence and turbulent scalar transport, and a stable channel side with relatively weak turbulence or laminar-like flow, weak turbulent scalar transport but large scalar fluctuations and steep mean scalar gradients. The distinct turbulent–laminar patterns observed at certain $Ro$ on the stable channel side induce similar patterns in the scalar field. The main conclusions of the study are that rotation reduces the similarity between the scalar and velocity field and that the Reynolds analogy for scalar-momentum transport does not hold for rotating turbulent channel flow. This is shown by a reduced correlation between velocity and scalar fluctuations, and a strongly reduced turbulent Prandtl number of less than 0.2 on the unstable channel side away from the wall at higher $Ro$. On the unstable channel side, scalar scales become larger than turbulence scales according to spectra and the turbulent scalar flux vector becomes more aligned with the mean scalar gradient owing to rotation. Budgets in the governing equations of the scalar energy and scalar fluxes are presented and discussed as well as other statistics relevant for turbulence modelling.