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Global linear and nonlinear stability of viscous confined plane wakes with co-flow
||Journal of Fluid Mechanics
The global stability of confined uniform density wakes is studied numerically, using
two-dimensional linear global modes and nonlinear direct numerical simulations. The
wake inflow velocity is varied between different amounts of co-flow (base bleed).
In accordance with previous studies, we find that the frequencies of both the most
unstable linear and the saturated nonlinear global mode increase with confinement.
For wake Reynolds number Re=100 we find the confinement to be stabilising,
decreasing the growth rate of the linear and the saturation amplitude of the nonlinear
modes. The dampening effect is connected to the streamwise development of the base
flow, and decreases for more parallel flows at higher Re. The linear analysis reveals
that the critical wake velocities are almost identical for unconfined and confined
wakes at Re ? 400. Further, the results are compared with literature data for an
inviscid parallel wake. The confined wake is found to be more stable than its inviscid
counterpart, whereas the unconfined wake is more unstable than the inviscid wake.
The main reason for both is the base flow development. A detailed comparison of the
linear and nonlinear results reveals that the most unstable linear global mode gives
in all cases an excellent prediction of the initial nonlinear behaviour and therefore
the stability boundary. However, the nonlinear saturated state is different, mainly
for higher Re. For Re=100, the saturated frequency differs less than 5% from the
linear frequency, and trends regarding confinement observed in the linear analysis are