POD analysis of coherent structures in forced turbulent flow over a fence

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).