PHYSICAL REVIEW FLUIDS 2, 103901 (2017) Understanding the destabilizing role for surface tension in planar shear flows in terms of wave interaction L. Biancofiore, 1 E. Heifetz, 2 J. Hoepffner, 3 and F. Gallaire 4 1 Department of Mechanical Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey 2 Department of Geophysics, School of Earth Sciences, Tel Aviv University, Tel Aviv, 69978, Israel 3 CNRS (UMR 7190), Université Pierre et Marie Curie, Institut Jean le Rond d’Alembert, 75005, Paris, France 4 EPFL/LFMI, Route Cantonale, Lausanne, CH-1015, Switzerland (Received 1 February 2017; published 4 October 2017) Both surface tension and buoyancy force in stable stratification act to restore perturbed interfaces back to their initial positions. Hence, both are intuitively considered as stabilizing agents. Nevertheless, the Taylor-Caulfield instability is a counterexample in which the presence of buoyancy forces in stable stratification destabilize shear flows. An explanation for this instability lies in the fact that stable stratification supports the existence of gravity waves. When two vertically separated gravity waves propagate horizontally against the shear, they may become phase locked and amplify each other to form a resonance instability. Surface tension is similar to buoyancy but its restoring mechanism is more efficient at small wavelengths. Here, we show how a modification of the Taylor-Caulfield configuration, including two interfaces between three stably stratified immiscible fluids, supports interfacial capillary gravity whose interaction yields resonance instability. Furthermore, when the three fluids have the same density, an instability arises solely due to a pure counterpropagating capillary wave resonance. The linear stability analysis predicts a maximum growth rate of the pure capillary wave instability for an intermediate value of surface tension corresponding to We −1 = 5, where We denotes the Weber number. We perform direct numerical nonlinear simulation of this flow and find nonlinear destabilization when 2  We −1  10, in good agreement with the linear stability analysis. The instability is present also when viscosity is introduced, although it is gradually damped and eventually quenched. DOI: 10.1103/PhysRevFluids.2.103901 I. INTRODUCTION Surface tension acts as a restoring force in shear flows. Perturbed interfaces tend to go back to their initial position under its restoring influence. For this reason, surface tension is often considered intuitively as a stabilizing force in plane shear flows. For instance, the effect of the surface tension at the interface of two immiscible fluids damps the Kelvin-Helmholtz instability [1,2]. In axisymmetric shear flows, however, the same reasoning does not hold true, and surface tension can become destabilizing as in the Rayleigh-Plateau instability [3,4] of a liquid jet. A destabilizing influence of surface tension was recently found in planar jets and wakes [5–7] by means of both linear global analysis and direct numerical simulations (DNS). This counterintuitive destabilization is caused by the appearance of a second unstable mode acting particularly at large wave numbers. The presence of this second unstable mode was explained by Biancofiore et al. [8] using the kernel wave (KW) perspective. This perspective was first developed in atmospheric science to explain the baroclinic instability mechanism for cyclone genesis resulting from interaction in a distance between Rossby waves [9]. The instability in flows featuring two distinct potential vorticity gradients can be interpreted in terms of the interaction between the two Rossby waves created at the vorticity edges. For a comprehensive review of the KW perspective, the reader is referred to Ref. [10]. The second mode destabilizing planar immiscible wakes can be interpreted as a Rossby-capillary instability [8], i.e., the interaction between the capillary waves at the interfaces with the Rossby waves created at the vorticity edges of the wake flow velocity profile. 2469-990X/2017/2(10)/103901(22) 103901-1 ©2017 American Physical Society