Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are 'minimal' in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, L z , which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (L x 2L z , L y L z ) to prevent other directions to be constrained as well. It is also found that very long boxes, L x 2L y , couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ∼ 20S −1 , and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggest that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a “velocity” that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size.

The three-dimensional vortex clusters, and the structures based on the quadrant classification of the intense tangential Reynolds stress (Qs), are studied in direct numerical simulations of statistically stationary homogeneous shear turbulence (HST) at Taylor microscale Reynolds number Re λ ≈ 50-250, with emphasis on comparisons with turbulent channels (CHs). The Qs and vortex clusters in HST are found to be versions of the corresponding detached (in the sense of del Álamo et al. (J. Fluid Mech., vol. 561 (2006), pp. 329-358)) structures in CHs, although statistically symmetrised with respect to the substitution of sweeps by ejections and vice versa. In turn, these are more symmetric versions of the corresponding attached Qs and clusters. In both flows, only co-gradient sweeps and ejections larger than the local Corrsin scale are found to couple with the shear. They are oriented anisotropically, and are responsible for carrying most of the total Reynolds stress. Most large eddies in CHs are attached to the wall, but it is shown that this is probably a geometric consequence of their size, rather than the reason for their dynamical significance. Most small Q structures associated with different quadrants are far from each other in comparison to their size, but those that are close to each other tend to form quasi-streamwise trains of groups of a sweep and an ejection paired side by side in the spanwise direction, with a vortex cluster in between, generalising to three dimensions the corresponding arrangement of attached eddies in CHs. These pairs are organised around an inclined large-scale conditional vortex 'roller', and it is shown that the composite structure tends to be located at the interface between high-and low-velocity streaks, as well as in strong 'co-gradient' shear layers that separate streaks of either sign in which velocity is more uniform. It is further found that the conditional rollers are terminated by 'hooks' reminiscent of hairpins, both upright and inverted. The inverted hook weakens as the structures approach the wall, while the upright one changes little. At the same time, the inclination of the roller with respect to the mean velocity decreases from 45 • in HST to quasi-streamwise for † Email address for correspondence: jimenez@torroja.

The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex shaped as an inverted hairpin followed by an upright hairpin. The asymmetry between the forward and backward cascade arises from the opposite flow circulation within the hairpins, which triggers reversed patterns in the flow.

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Background The optimal hypothermic level in total arch replacement with stented elephant trunk implantation for acute type A aortic dissection (aTAAD) has not been established, and the superiority of unilateral or bilateral cerebral perfusion remains a controversial issue. Therefore, we evaluated the application of moderate hypothermic circulatory arrest (MHCA) with a core temperature of 29 °C and bilateral selective antegrade cerebral perfusion in aTAAD treated by total arch replacement with stented elephant trunk implantation. Methods From July 2019 to January 2020, 25 aTAAD patients underwent total arch replacement with stented elephant trunk implantation via MHCA (29 °C) and bilateral selective antegrade cerebral perfusion (modified group). Thirty-six patients treated by the same procedure with MHCA (25 °C) and unilateral selective antegrade cerebral perfusion during this period were selected as controls. Results There were no differences between the two groups of patients in terms of age, sex, incidence of hypertension, malperfusion, and pericardial effusion, although the incidence of cardiac tamponade was higher in the modified group (control 2.8%, modified 20%; P = 0.038). The lowest mean circulatory arrest temperature was 24.6 ± 0.9 °C in the control group, and 29 ± 0.8 °C in the modified group (P <  0.001). In-hospital mortality was 4.9% (3/61) for the entire cohort (control 8.3%, modified 0; P = 0.262). The incidence of permanent neurologic deficit was 4.9% (control 8.3%, modified 0; P = 0.262). There were no significant differences in the occurrence of temporary neurological deficit, renal failure, and paraplegia between groups. The rate of major adverse events in the modified group was lower (30.6% vs. 4%, P = 0.019). A shorter duration of ventilation and ICU stay was identified in the modified group, as well as a reduced volume of drainage within the first 48 h and red blood cell transfusion. Conclusions The early results of MHCA (29 °C) and bilateral selective antegrade cerebral perfusion applied in total arch replacement with stented elephant trunk implantation for aTAAD were acceptable, providing similar inferior cerebral and visceral protection compared with that of the conventional strategy. A higher core temperature may account for the shorter duration of ventilation and ICU stay, as well as a reduced volume of drainage and red blood cell transfusion.

To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral, or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow nonnormality. This nonnormality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this new type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wavenumber area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance -Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86 and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [“Extremely high wall-shear stress events in a turbulent boundary layer,” J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [“Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions,” J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions.