======Turbulent Stokes Boundary Layer======
=====LES by Salon, Armenio and Crise=====

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====Description====

Large-eddy simulations (LES) are employed to investigate the Stokes boundary layer in the 
turbulent regime. The flow is driven by an harmonic pressure gradient in the x-direction: 
\[ \frac{dP}{dx}(t) = -U_o \omega \cos(\omega t)  \]
where \(P\) is the kinematic pressure, \(U_o\) is the maximum amplitude of the outer velocity and 
\(\omega\) is the angular frequency of the oscillations. The Reynolds number is defined as 
\[ Re_{\delta} = \frac{U_o \delta_s}{\nu} \]
where \(\delta_s = \sqrt{2\nu/\omega}\) is the Stokes-layer thickness and \(\nu\)
is the kinematic viscosity.

The Reynolds number investigated is \(Re_{\delta} = 1790\),
that corresponds to test number 8 of the experimental study carried out by Jensen et al. (1989); at 
this \(Re_{\delta}\) turbulence is present in most of the oscillation cycle.

Boundary conditions are no-slip at the bottom wall and free-slip at the top boundary, as
shown in <imgref cas85-geom>. Due to the homogeneity in the spanwise and streamwise directions, 
periodic boundary conditions are taken there. 
The initial condition is set by starting the oscillatory motion from the fluctuating 
three-dimensional components of a steady fully-developed turbulent flow field. The statistics were 
accumulated over 15 complete cycles, by averaging over the (x,y)-planes of homogeneity, and in 
phase over half-cycle (ensemble average), since the flow field repeats every half-cycle with the 
sign of the streamwise velocity reversed. Thus 30 half-cycles were used for each phase of the 
oscillation.

<imgcaption cas85-geom|Flow configuration>{{ figs:case085:case-geom.png |Flow configuration}}</imgcaption>

====Simulation Details====

Flow geometry and coordinate system are sketched in <imgref cas85-geom>. Several grid resolutions were 
considered in the LES study. Here we present data from grid C4 that has the following
computational parameters: \(L_x = 50 \delta_s\), \(L_y = 25 \delta_s\), \(L_z = 40 \delta_s\), with
96x96x256 grid cells respectively in the \(x\), \(y\), \(z\) directions and non-dimensional grid 
spacing equal to: \(\Delta x^+ = 41\), \(\Delta y^+ = 21\), \(\Delta z^+_{min} = 2\), 
\(\Delta z^+_{max} = 22\). 

====Available Results====

The available data consists of phase-averaged profiles of the rms fluctuating velocities
\(u'\), \(v'\), \(w'\) and the shear stress \(\overline{uw}\) at 12 phase angles of 15<sup>o</sup>, 
30<sup>o</sup>, 45<sup>o</sup>, 60<sup>o</sup>, 75<sup>o</sup>, 90<sup>o</sup>, 105<sup>o</sup>, 
120<sup>o</sup>, 135<sup>o</sup>, 150<sup>o</sup>, 165<sup>o</sup> and 180<sup>o</sup>.

Velocities are normalized by \(U_o\), and the wall normal distance by the Stokes thickness, \(\delta_s\).

[[case085-plots|Sample plots]] of selected quantities are available.

The data files can be downloaded as compressed archives, or individually from the 
tables below.

  * {{cdata:case085:tsbl-allfiles.zip|tsbl-allfiles.zip}}
  * {{cdata:case085:tsbl-allfiles.tar.gz|tsbl-allfiles.tar.gz}}

^ Flow Quantity  ^  File  ^
| Rms \(u'\) velocity             |  {{cdata:case085:u_rms_mean.dat|u_rms_mean.dat}}  |
| Rms \(v'\) velocity             |  {{cdata:case085:v_rms_mean.dat|v_rms_mean.dat}}  |
| Rms \(w'\) velocity             |  {{cdata:case085:w_rms_mean.dat|w_rms_mean.dat}}  |
| Shear stress \(\overline{uw}\)  |  {{cdata:case085:uw_mean.dat|uw_mean.dat}}        |


====References====

  - Jensen, B.L.,  Sumer, B.M., Fredsoe, J. (1989). [[https://doi.org/10.1017/S0022112089002302|Turbulent oscillatory boundary layers at high Reynolds numbers]]. //J. Fluid Mech.//, Vol. 206, p. 265.
  - Salon, S., Armenio, V., Crise, A. (2007). [[https://doi.org/10.1017/S0022112006003053|A numerical investigation of the Stokes boundary layer in the turbulent regime]]. //J. Fluid Mech.//, Vol. 570, pp. 253-296.

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Indexed data:
<data dbcase semi_confined_flow>
case       : 085
title      : Turbulent Stokes boundary layer
author*    : Salon, Armenio, Crise
year       : 2007
type       : LES
flow_tag*  : unsteady, 2dbl
</data>