From large-eddy simulations of unforced and forced turbulent boundary layer
flow over a surface-mounted fence of height h (Re-h = 3000) periodic sampl
es have been collected. These samples (snapshots) have been used to carry o
ut three-dimensional proper orthogonal decompositions (POD), in order to ex
tract the dominating spatio-temporal structures of the flow.
Results from high-frequency and low-frequency forced cases are compared as
are the results from the unforced reference case. The forcing was carried o
ut via time-periodic blowing/suction through a crosswind slot about three f
ence heights in front of the flow obstacle. The high-frequency forcing (wit
h Str(h) = 0.60) supports the shear layer roll-up and the pairing phase. Th
e low-frequency forcing (with Str(h) = 0.08) supports the ejection of large
-scale structures from the separation bubble. In each case, the correspondi
ng forcing mode can be identified with a spatio-temporal pair of modes (wit
h phase shifts in space and time) representing a downstream travelling wave
.
From a Galerkin projection of the Navier-Stokes equation onto the POD modes
, the energy balance equation can be derived for an individual mode. An eva
luation of the nonlinear energy transfer term shows that the roll-up proces
s in the separated shear layer receives most of the energy from the mean fl
ow and exchanges little energy with the other modes. In comparison to this,
the vortex shedding from the recirculation bubble receives larger amounts
of energy from the mean flow and in addition, exchanges one order of magnit
ude larger amounts of energy with the 'neighbouring' modes. This also expla
ins why, in our flow case, the low-frequency forcing (with Str(h) = 0.08) l
eads to a much stronger reduction of the mean re-attachment length (36%) th
an the high-frequency forcing (with Str(h) = 0.60).