Response of noise-amplifier flows: From linear control to nonlinear jet breakup

Among hydrodynamically unstable flows, the amplifier-flows are characterized by their large amplification potential in presence of external noise. Since amplifiers do not have an intrinsic dynamics, a chosen forcing can be applied to eventually control the downstream evolution of such flows. With this aim, we intend to analyse the flow control in amplifier-flows, common examples being the flow in a backward facing step and the free surface capillary jet. We begin by analysing the flow control applied over a three-dimensional spanwise-modulating backward facing step. With the objective of reducing the lower recirculation length, we look for small amplitude optimal controls either by blowing/suction or by applying a wall deformation.

A similar approach is then applied for the free surface axisymmetric capillary jet. The analysis is simplified by using the one-dimensional equations of Eggers & Dupont (J. Fluid Mech., vol. 262, 1994, 205-221) which describe the flow using only the radius of the jet and its velocity as functions of the jet axial coordinate and time. We concentrate on two jet variations, one has a parallel base flow and the other has a spatially varying base flow due to the stretching effect of gravity. A local stability analysis is sufficient for analysing parallel base flows, whereas the spatially varying jets are analysed in the global framework. Further, we perform numerical simulations with the target of finding the optimal forcing which minimizes the intact jet length, also referred to as the breakup length. Unlike the parallel jets, the optimal forcing frequency for the spatially varying jet is dependent on the forcing amplitude. Similar results are then captured through the global resolvent analysis by introducing the forcing amplitude in the linear resolvent framework. Using a similar linear stability approach we then analyse the special case of silicone-in-silica jets inspired by the experimental results of Gumennik et al. (Nat. Commun., vol. 4, 2013, 2216). Based on the reformulated one-dimensional equations, we predict numerically the drop size as a function given fibre feed speed, which is found to be in close accordance with the experimental results.

Finally, we explore experimentally the physical dynamics of drops rising in an external medium in a Hele-Shaw cell due to buoyancy. We specifically analyse the relation between the drop velocity and the mean film thickness magnitude around the drop. We present complete film thickness maps for these drops which highlight the 'catamaran' like shape often observed for similar drops in pressure driven flows inside the Hele-Shaw cell.