[Paper Review] Direct numerical simulation of the very large anisotropic scales in a turbulent channel

Juan C. del Álamo, Javier Jiménez|arXiv (Cornell University)|Sep 9, 2013

Fluid Dynamics and Turbulent Flows12 references21 citations

TL;DR

This study presents the first direct numerical simulation of turbulent channel flow at Reτ = 550 with a sufficiently large computational domain to resolve very large anisotropic scales (VLAS) in the outer layer. Using spectral methods and high-resolution grids, it demonstrates that VLAS carry substantial kinetic energy and Reynolds stresses, challenging prior assumptions that they are 'inactive' and confirming their role as active, momentum-transferring structures in wall-bounded turbulence.

ABSTRACT

Over the last decades the knowledge on the small scales of turbulent wall flows has experienced a significant advance, especially in the near-wall region where the highest production of turbulent energy and the maximum turbulence intensity occur. The development of computers has played an important role in this progress, making direct numerical simulations affordable (Kim, Moin & Moser, 1987), and offering wider observational possibilities than most laboratory experiments. The large scales have received less attention, and it has not been until recently that their significance and their real size have been widely recognized, thanks in part to the experiments by Hites (1997) and Kim & Adrian (1999), and to the compilation of experimental and numerical data by Jimenez (1998). The requirements of both a very large box and a high Reynolds number has made direct numerical simulation of the VLAS unapproachable until today. The purpose of this report is to serve as a preliminary description of a newly compiled numerical database of the characteristics of the large scales in turbulent channel flow at moderate Reynolds numbers.

Motivation & Objective

• To resolve the very large anisotropic scales (VLAS) in turbulent channel flow, which have been neglected due to their large size and computational cost.
• To investigate whether VLAS are truly 'inactive' as previously assumed, particularly in terms of carrying Reynolds stresses and turbulent energy.
• To determine the scaling and spatial characteristics of VLAS in the outer layer of the flow using high-resolution direct numerical simulation.
• To assess the role of VLAS in momentum transport and their potential influence on near-wall turbulence scaling behavior.
• To provide a benchmark numerical database for future studies on large-scale structures in wall-bounded turbulence.

Proposed method

• Conduct direct numerical simulations (DNS) of incompressible turbulent flow in a plane channel at Reτ = 550 and Reτ = 180 using a fully spectral numerical code.
• Employ dealiased Fourier expansions in streamwise and spanwise directions and Chebyshev polynomials in the wall-normal direction for high accuracy.
• Use a large computational domain of size 8πh × 2h × 4πh (Lx × Ly × Lz) to avoid artificial confinement of the largest structures.
• Compute premultiplied one-dimensional spectra (kxEuu1D, kzEww1D) and energy distribution across scales to identify VLAS characteristics.
• Analyze the structure parameter σuv = Euv / (Euu E vv)1/2 to quantify momentum transport efficiency of large-scale motions.
• Compare results with prior simulations (e.g., Moser et al., 1999) and experimental data to validate the resolution and physical fidelity of the VLAS representation.

Experimental results

Research questions

• RQ1 Do very large anisotropic scales (VLAS) in turbulent channel flow carry significant turbulent kinetic energy and Reynolds stresses, contradicting the 'inactive' assumption?
• RQ2 How do the spatial scales and energy distribution of VLAS vary with wall-normal distance and Reynolds number?
• RQ3 What is the role of VLAS in momentum transport, as quantified by the structure parameter σuv?
• RQ4 Can the observed VLAS be explained by a wake model originating from decaying isotropic structures?
• RQ5 To what extent do VLAS influence the scaling of near-wall turbulence statistics, such as ⟨u′²⟩?

Key findings

• The VLAS in the outer layer of the turbulent channel flow extend up to 2–5h in streamwise length and carry a substantial fraction of the total turbulent kinetic energy.
• Premultiplied one-dimensional spectra show two distinct peaks: one in wall units (buffer layer streaks) and a second in outer units (VLAS), which strengthens with increasing Reynolds number.
• The structure parameter σuv approaches unity for VLAS, indicating they are highly efficient in transporting momentum and thus 'active' in Townsend’s sense.
• VLAS are found to be very high and capable of reaching the walls, potentially explaining the Reynolds number dependence of near-wall turbulence intensity.
• The energy in the wall-normal velocity component v decays as 1/λx for very long wavelengths, but the cospectrum behavior depends critically on σuv, which remains high for VLAS.
• The wake model proposed explains VLAS as the convected, decaying wakes of compact isotropic structures, suggesting a physical origin for their anisotropy and longevity.