Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session E04: Turbulence: Wall-Bounded Flows II: Linearized and Quasilinear Approaches
2:45 PM–4:55 PM,
Sunday, November 21, 2021
Room: North 121 B
Chair: Beverley McKeon, Caltech
Abstract: E04.00007 : On the Wall Pressure and Shear Stress Spectra in Turbulent Boundary Layers*
4:03 PM–4:16 PM
Presenter:
Anthony Leonard
(California Institute of Technology)
Authors:
Anthony Leonard
(California Institute of Technology)
Simon S Toedtli
(California Institute of Technology)
Beverley J McKeon
(California Institute of Technology)
numerical simulations of incompressible turbulent channel flow at Reτ = 180. One observation of these
results is that the spectra are primarily limited to small wavenumbers , e.g., the spectrum of ∂u/∂y is essentially
confined to kx h ≦ 2 and kz h ≦ 16, where h is the channel half-width.
In an attempt to better understand the results of the above simulations, we write the shear stress spectra in
terms of the spectrum of ∂2v/∂y2, the spectrum of ∂ωy/∂y , and their cross spectrum, all at the wall.
It is then shown, in a manner that is very much akin to resolvent analysis, that the
latter three can be estimated using the (kx,kz) dependence of the dominant eigenfunctions, i.e., those with the
smallest time-decay rates, of the Orr-Sommerfeld/Squire system and their eigenvalues.
In the case of pressure fluctuations, the spectra of the Stokes pressure, of the rapid part of the inertial
pressure, and of their sum are determined using the same methodology. The contribution of the slow part of the
inertial pressure, however, requires further nonlinear analysis.
The overall result is potentially a low-order model of turbulence fluctuations at the wall.
*ONR grant # N00014-17-1-3022 is gratefully acknowledged
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