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Institute of Fluid Dynamics
ETH Zurich
Abstract-
Flows over protruding steps or ribs occur in many technical devices as well
as in geophysical problems. At low Reynolds number Re, the flow over a step
develops closed 2-D recirculation regions in front as well as downstream of
the step. With Re increasing to the order of a few hundred (based on step
height and bulk velocity), the flow invariably becomes three-dimensional,
developing pronounced streamwise vortices and streaks originating at the step.
In the present work, the flow over a rectangular step in a plane channel
has been investigated. An accurate spectral element discretization in the
streamwise and wall-normal directions and a Fourier spectral method in the
spanwise direction is used. The singularity at the step corner is treated
by a special local grid refinement.
2-D simulations were performed in order to clarify the scaling of length
and height of the separated regions with the Reynolds number. At low Re
(creeping flow) these dimensions are nearly constant, while they increase
algebraically at higher Re.
A linear-stability analysis and high-resolution 3-D simulations have been
performed to investigate the mechanisms behind the formation of intense
three-dimensional vortices at the step. It is demonstrated that the
three-dimensionality is not induced by an absolute instability as was
suggested previously, but rather is caused by minute disturbances in the
oncoming flow which are amplified in the step region. A smooth transition
from an almost 2-D to a 3-D flow is observed if the inflow disturbance
level is gradually increased, with the disturbance amplitude at the step
depending linearly on the inflow disturbance amplitude. Consequently, under
the considered conditions no critical threshold is found below which the
flow would remain two-dimensional. The structure of the computed 3-D flow
is found to be in good agreement with experimental results.
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