Adrián Lozano-Durán

Effect of the computational domain on direct simulations of turbulent channels up to Reτ = 4200

The effect of domain size on direct numerical simulations of turbulent channels with periodic boundary conditions is studied. New simulations are presented up to Reτ = 4179 in boxes with streamwise and spanwise sizes of 2πh × πh, where h is the channel half-height. It is found that this domain is large enough to reproduce the one-point statistics of larger boxes. A simulation in a box of size 60πh × 6πh is used to show that a contour of the two-dimensional premultiplied spectrum of the streamwise velocity containing 80% of the kinetic energy closes at λx ≈ 100h.

Aspect ratio effects in turbulent duct flows studied through direct numerical simulation

Three-dimensional effects in turbulent duct flows, i.e., sidewall boundary layers and secondary motions, are studied by means of direct numerical simulation (DNS). The spectral element code Nek5000 is used to compute turbulent duct flows with aspect ratios 1–7 (at Reb, c = 2800, Reτ, c ≃ 180) and aspect ratio 1 (at Reb, c = 5600, Reτ, c ≃ 330), in streamwise-periodic boxes of length 25h. The total number of grid points ranges from 28 to 145 million, and the pressure gradient is adjusted iteratively in order to keep the same bulk Reynolds number in the centreplane with changing aspect ratio. Turbulence is initiated via a trip forcing active during the initial stages of the simulation, and the statistical convergence of the data is discussed both in terms of transient approach and averaging period. Spanwise variations in wall shear, mean-flow profiles, and turbulence statistics are analysed as a function of aspect ratio, and also compared with the spanwise-periodic channel (as idealisation of an infinite as...

A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow

The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in various physical systems. An example implementation of SSD is the second order closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence and specifically the emergence and maintenance of the roll/streak structure. This closure eliminates nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. Here, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted nonlinear (RNL) system. RNL simulations reveal that the essential features of wall-turbulence dynamics are retained. Remarkably, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components giving rise to a naturally minimal representation of its turbulence dynamics. Although greatly simplified, this RNL turbulence exhibits natural-looking structures and statistics. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed the RNL system continues to produce self-sustaining turbulent structure and dynamics. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very-large-scale structure (VLSM) in the outer layer. Diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS.

Turbulence in the highly restricted dynamics of a closure at second order: comparison with DNS

S3T (Stochastic Structural Stability Theory) employs a closure at second order to obtain the dynamics of the statistical mean turbulent state. When S3T is implemented as a coupled set of equations for the streamwise mean and perturbation states, nonlinearity in the dynamics is restricted to interaction between the mean and perturbations. The S3T statistical mean state dynamics can be approximately implemented by similarly restricting the dynamics used in a direct numerical simulation (DNS) of the full Navier-Stokes equations (referred to as the NS system). Although this restricted nonlinear system (referred to as the RNL system) is greatly simplified in its dynamics in comparison to the associated NS, it nevertheless self-sustains a turbulent state in wall-bounded shear flow with structures and dynamics comparable to those observed in turbulence. Moreover, RNL turbulence can be analysed effectively using theoretical methods developed to study the closely related S3T system. In order to better understand RNL turbulence and its relation to NS turbulence, an extensive comparison is made of diagnostics of structure and dynamics in these systems. Although quantitative differences are found, the results show that turbulence in the RNL system closely parallels that in NS and suggest that the S3T/RNL system provides a promising reduced complexity model for studying turbulence in wall-bounded shear flows.

Time-resolved Evolution of the Wall-bounded Vorticity Cascade

The temporal evolution of vortex clusters in a turbulent channel at Re? = 950 is studied using DNS sequences with temporal separations among fields short enough for individual structures to be tracked. From the geometric intersection of structures in consecutive fields, we build temporal connection graphs of all the vortex clusters, and, from their properties, define main and secondary branches for each evolution. It is found that the average lifetime of the clusters within a branch is proportional to the cube root of their maximum volumes, and that they move approximately with the local mean velocity. Especial attention is paid to their wall-normal displacement. It is found that their probability of moving away from the wall is only slightly higher than that of moving towards it, and that this behaviour is independent of the wall distance at which the branch is initially created. Finally, direct and inverse physical cascades are defined, associated with the splits and mergers between structures. It is found that the direct cascade predominates, but that both directions are roughly comparable.

Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at a friction Reynolds number of 932

The invariants of the velocity gradient tensor,

Algorithm 964: An Efficient Algorithm to Compute the Genus of Discrete Surfaces and Applications to Turbulent Flows

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Numerically accurate computation of the conditional trajectories of the topological invariants in turbulent flows

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A POD-based analysis of turbulence in the reduced nonlinear dynamics system

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Coherent Structures in Wall-Bounded Turbulence

, and their enstrophy and strain components are studied in the logarithmic layer of an incompressible turbulent channel flow. The velocities are filtered in the three spatial directions and the results are analysed at different scales. We show that the