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The linear spatiotemporal response to an infinitesimal disturbance is analyzed for an electrified falling film based on the Orr-Sommerfeld boundary value problem. Four spatial branches are identified, which lose their spatial symmetry in the presence of an electric field. In addition, the absolute and convective instabilities are studied within the frameworks of the saddle point approach and the collision criterion. The collision criterion offers two unstable branches that characterize the exact range of the unstable wave packet that is diminished in the presence of an electric field. In contrast, the saddle point approach offers only one unstable branch. The associated unstable range of the wave packet is similar to that predicted by the collision criterion only when the electric field is enhanced. It is shown that the electrified falling film is convectively unstable., QC 20160220

Direct numerical simulations of the fully developed turbulent flow through a porous channel and duct are performed based on the spectral element code Nek5000. The volume-averaged Navier-Stokes (VANS) equations are implemented in order to describe the flow in the composite medium. The numerical simulations of the VANS equations are carried out at a constant value of the bulk Reynolds number when the porosity, or equivalently, the permeability of the medium varies successively. The mean and turbulent energy budgets are computed and the effect of porosity on the secondary flow in a duct is examined., QC 20200616

Direct numerical simulations of the fully developed turbulent flow through a porous square duct are performed to study the effect of the permeable wall on the secondary cross-stream flow. The volume-averaged Navier-Stokes equations are used to describe the flow in the porous phase, a packed bed with porosity epsilon(c) = 0.95. The porous square duct is computed at Re-b similar or equal to 5000 and compared with the numerical simulations of a turbulent duct with four solid walls. The two boundary layers on the top wall and porous interface merge close to the centre of the duct, as opposed to the channel, because the sidewall boundary layers inhibit the growth of the shear layer over the porous interface. The most relevant feature in the porous duct is the enhanced magnitude of the secondary flow, which exceeds that of a regular duct by a factor of four. This is related to the increased vertical velocity, and the different interaction between the ejections from the sidewalls and the porous medium. We also report a significant decrease in the streamwise turbulence intensity over the porous wall of the duct (which is also observed in a porous channel), and the appearance of short spanwise rollers in the buffer layer, replacing the streaky structures of wall-bounded turbulence. These spanwise rollers most probably result from a Kelvin-Helmholtz type of instability, and their width is limited by the presence of the sidewalls., QC 20160112

The study of a film falling down an inclined plane is revisited in the presence of imposed shear stress. Earlier studies regarding this topic (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469-485; Wei, Phys. Fluids, vol. 17, 2005a, 012103), developed on the basis of a low Reynolds number, are extended up to moderate values of the Reynolds number. The mechanism of the primary instability is provided under the framework of a two-wave structure, which is normally a combination of kinematic and dynamic waves. In general, the primary instability appears when the kinematic wave speed exceeds the speed of dynamic waves. An equality criterion between their speeds yields the neutral stability condition. Similarly, it is revealed that the nonlinear travelling wave solutions also depend on the kinematic and dynamic wave speeds, and an equality criterion between the speeds leads to an analytical expression for the speed of a family of travelling waves as a function of the Froude number. This new analytical result is compared with numerical prediction, and an excellent agreement is achieved. Direct numerical simulations of the low-dimensional model have been performed in order to analyse the spatiotemporal behaviour of nonlinear waves by applying a constant shear stress in the upstream and downstream directions. It is noticed that the presence of imposed shear stress in the upstream (downstream) direction makes the evolution of spatially growing waves weaker (stronger)., QC 20141010

The effect of insoluble surfactants on the instability of a two-layer film flow down an inclined plane is investigated based on the Orr-Sommerfeld boundary value problem. The study, focusing on Stokes flow [P. Gao and X.-Y. Lu, "Effect of surfactants on the inertialess instability of a two-layer film flow," J. Fluid Mech. 591, 495-507 (2007)], is further extended by including the inertial effect. The surface mode is recognized along with the interface mode. The initial growth rate corresponding to the interface mode accelerates at sufficiently long-wave regime in the presence of surface surfactant. However, the maximum growth rate corresponding to both interface and surface modes decelerates in the presence of surface surfactant when the upper layer is more viscous than the lower layer. On the other hand, when the upper layer is less viscous than the lower layer, a new interfacial instability develops due to the inertial effect and becomes weaker in the presence of interfacial surfactant. In the limit of negligible surface and interfacial tensions, respectively, two successive peaks of temporal growth rate appear in the long-wave and short-wave regimes when the interface mode is analyzed. However, in the case of the surface mode, only the long-wave peak appears., QC 20141111