We compute the optimal transient growth of perturbations sustained by a turbulent channel flow following the same approach recently used by del Álamo and Jiménez ͓J. Fluid Mech. 559, 205 ͑2006͔͒. Contrary to this previous analysis, we use generalized Orr-Sommerfeld and Squire operators consistent with previous investigations of mean flows with variable viscosity. The optimal perturbations are streamwise vortices evolving into streamwise streaks. In accordance with del Álamo and Jiménez, it is found that for very elongated structures and for sufficiently large Reynolds numbers, the optimal energy growth presents a primary peak in the spanwise wavelength, scaling in outer units, and a secondary peak scaling in inner units and corresponding to z + Ϸ 100. Contrary to the previous results, however, it is found that the maximum energy growth associated with the primary peak increases with the Reynolds number. This growth, in a first approximation, scales linearly with an effective Reynolds number based on the centerline velocity, the channel half width and the maximum eddy viscosity associated. The optimal streaks associated with the primary peak have an optimal spacing of z =4h and scale in outer units in the outer region and in wall units in the near wall region, where they still have up to 50% of their maximum amplitude near y + = 10.

Direct numerical simulations of stably stratified, turbulent channel flow at low to moderate Reynolds number have been performed using large computational boxes and considering a wide range of stratification levels. For weak stratification or high Reynolds number, the turbulence is affected by buoyancy in the core of the channel, but the near-wall region differs little from the neutral case. With strong stratification, large laminar patches appear in the near-wall region and turbulent momentum and buoyancy fluxes vanish in the core of the channel. With increasing stratification, the near-wall streaks remain essentially unmodified, while large-scale global modes are damped. In the central region, internal gravity waves are dominant. In addition, there is an intermediate outer layer where the dynamics of the turbulent structures is governed by local fluxes. In this region, energy spectra collapse when using local Obukhov scaling.

Atrial fibrillation (AF) alters left atrial (LA) hemodynamics, which can lead to thrombosis in the left atrial appendage (LAA), systemic embolism and stroke. A personalized risk-stratification of AF patients for stroke would permit improved balancing of preventive anticoagulation therapies against bleeding risk. We investigated how LA anatomy and function impact LA and LAA hemodynamics, and explored whether patient-specific analysis by computational fluid dynamics (CFD) can predict the risk of LAA thrombosis. We analyzed 4D-CT acquisitions of LA wall motion with an in-house immersed-boundary CFD solver. We considered six patients with diverse atrial function, three with either a LAA thrombus (removed digitally before running the simulations) or a history of transient ischemic attacks (LAAT/TIA-pos), and three without a LAA thrombus or TIA (LAAT/TIA-neg). We found that blood inside the left atrial appendage of LAAT/TIA-pos patients had marked alterations in residence time and kinetic energy when compared with LAAT/TIA-neg patients. In addition, we showed how the LA conduit, reservoir and booster functions distinctly affect LA and LAA hemodynamics. Finally, fixed-wall and moving-wall simulations produced different LA hemodynamics and residence time predictions for each patient. Consequently, fixed-wall simulations risk-stratified our small cohort for LAA thrombosis worse than moving-wall simulations, particularly patients with intermediate LAA residence time. Overall, these results suggest that both wall kinetics and LAA morphology contribute to LAA blood stasis and thrombosis.

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