*Memoirs of the Graduate School of Engineering Kobe University,* No. 1, pp. 9-41, 2009

doi:10.5047/gseku.e.2009.004

## Direct Numerical Simulation and Filtering of Turbulent Flows over Model
Rough Surfaces

Akihiko NAKAYAMA^{1}, Koji SAKIO^{2} , Yuya KITANO^{2} and
Satoshi YOKOJIMA^{3}

^{1}Department of Civil Engineering, Kobe University

^{2}Software Cradle

^{3}Department of Systems Engineering, Shizuoka University

(Received November 20, 2009; Accepted February 26, 2010; Online published March 17, 2010)

Keywords: Turbulence, DNS, Rough Surface, Channel Flow, Large Eddies

Large-scale structures of flows over flat and wavy surfaces with and without two-dimensional and three-dimensional
roughness waves on them, are studied numerically by first conducting Direct Numerical Simulation (DNS) of these flows at
a Reynolds number in transitionally rough regime and numerically filtering the simulated results. A normalized kernel
filter with a few different sizes and shapes that are applicable to flows near wall are used. The normalized positive filter
smoothes the flow and the boundary by removing small-scale fluctuations and small-scale boundary protrusions at the
same time. The characteristics of the extracted large-scale flows over the smoothed boundary and the effects of the
removed sub-filter scale effects are studied in detail. Special emphasis is placed on the implications of the analyzed results
in development and improvement of approximate simulation methods like Large Eddy Simulation (LES) of turbulent
flows, where details of the flow and the boundary geometry cannot be resolved in full and modeling is needed. Filters with
sizes that correspond to typical LES grid sizes remove considerable fraction of total fluctuations including correlated ones
but the qualitative large structures are generally retained well if appropriate shape of the filter is used. The filtered
large-scale flows over rough surfaces have similarities with the filtered flow over smooth surface with added resistance due
to smoothed boundary. The effects of small boundary geometry removed by filtering are scaled by the filter size and the
magnitude of the local velocity. Basic filtered equations of motion for near wall flows are also derived that can be used for
rigorous analysis and modeling of interactions of the filter and the boundary.

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