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 : a low- and a high- regime. In the low- regime, the critical Reynolds number and critical streamwise wavenumber are proportional to, while the critical spanwise wavenumber is constant. In the high- regime, as, we find and for streamwise-rotating PPF, and and for streamwise-rotating PCF, with. 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 and at in streamwise-rotating PPF and PCF coincide with the minimum 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 and PCF at. We explain this similarity through an analysis of the perturbation equations. Consequently, the linear stability of streamwise-rotating PCF at large is closely related to that of spanwise-rotating PCF and Rayleigh-Bénard convection, with, where is the critical Rayleigh number. To explore the potential for subcritical transitions, direct numerical simulations were performed. At low, a subcritical transition regime emerges, characterised by large-scale turbulent-laminar patterns in streamwise-rotating PPF and PCF. However, at higher, subcritical transitions do not occur and the flow relaminarises for. Furthermore, we identify a narrow range where turbulent-laminar patterns develop under supercritical conditions.

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.

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.

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. 

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 comparedto 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 ABLsuch 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 awide range of stable and moderately unstable stratifications.

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