The non-normality of the Orr–Sommerfeld equation leads to the possibility of disturbance growth even though all eigenvalues are stable. In single-fluid flow the disturbance growth converges to a limit once the number of modes exceeds a minimum number. In the case of a two-fluid flow, however, convergence is not found. The problem of nonconvergence is due to the presence of the interface and the corresponding interfacial mode. The interface is replaced with a miscible layer of variable viscosity. When the thickness of the miscible layer is approximately equal to the thickness of the critical layer, the flow resembles two-fluid flow and one of the modes starts behaving like the interfacial mode.

In this paper we conduct a linear stability analysis of three-dimensional two-fluid flows and use an energy method to comment on its stability. The governing equations are solved using a Chebyshev-tau D 2 method that reduces the order of the coupled governing Orr-Sommerfeld and Squire equation and hence achieves more accurate results. A new norm, called the M-norm, is defined to overcome the problem of nonconvergence of the disturbance energy. The maximum amplification of O͑10 3 ͒ is achieved for streamwise independent disturbances due to the "lift-up effect," as is the case of three-dimensional single-fluid flow. In contrast to two-dimensional flows, where the adjoint of the leading mode influences the growth, the three-dimensional single-fluid flow growth is influenced by the adjoint of the second mode. Although most growth in three-dimensional two-fluid flow is due to the contribution of the adjoint of the second mode, at large time the interfacial mode contributes to most growth.

International audienceLinear stability analysis of a dielectric fluid confined in a cylindrical annulus of infinite length is performed under microgravity conditions. A radial temperature gradient and a high alternating electric field imposed over the gap induce an effective gravity that can lead to a thermal convection even in the absence of the terrestrial gravity. The linearized governing equations are discretized using a spectral collocation method on Chebyshev polynomials to compute marginal stability curves and the critical parameters of instability. The critical parameters are independent of the Prandtl number, but they depend on the curvature of the system. The critical modes are non-axisymmetric and are made of stationary helices

Purpose-The lattice Boltzmann (LB) method offers an alternative to conventional computational fluid dynamics (CFD) methods. However, its practical use for complex turbulent flows of engineering interest is still at an early stage. In this article, a LB wallmodeled large-eddy simulation (WMLES) solver is outlined. The flow past a rod-airfoil tandem in the sub-critical turbulent regime is examined as a challenging benchmark. Design/methodology/approach-Fluid dynamics are discretized upon the LB principles. The large-eddy simulation is accounted straightforwardly by including a modeled subgrid-scale viscosity in the LB scheme, whereas a wall-law model enforces the boundary condition at the first off-wall node. This physical modeling is briefly introduced and relevant references are given for details. The flow past a rod-airfoil tandem at Reynolds number Re = 4.8 × 10 4 and Mach number Ma 0.2 is simulated on a composite multiresolution grid; the numerical setup is detailed. Unsteady aerodynamic and aeroacoustic features including spectral analysis and far-field pressure fluctuations are discussed. Findings-Extensive quantitative comparisons with both experimental and numerical reference data indicate that aerodynamic and aeroacoustic features are well captured by the LB simulation. Originality/value-Our study shows that WMLES within the LB framework provides a workable and efficient alternative to Navier-Stokes CFD solvers in the context of complex turbulent flows. The LB method permits to access an attractive turnaround time while 1 preserving engineering accuracy.