A novel method for the analysis of hydrodynamic stability of flows is presented in which the 3D linearised perturbation equations are solved using numerical simulations (DS-LPE). The linear stability characteristics of two kinds of spatially evolving flows with slip boundaries are analysed to demonstrate the fidelity of the DS-LPE method, (1) flow over a flat plate with a porous lamination and (2) flow past a square slip cylinder. In-house codes solving the 3D linearised perturbation equations and Navier-Stokes equations (DS-NS) are developed to compute the perturbation and base flow solutions,
respectively. The influence of slip on the flow dynamics in the above two flows and the flow regime characterisations for the various control parameters are studied. The linear stability characteristics are examined by adding divergence-free temporal Fourier mode perturbations into the flow and inspecting their evolution in space and time. The
transient energy growth of the perturbations is used as the metric to identify the stability of the flow. The investigations of absolute and convective types of instabilities in the flow are also performed by probing the local evolution of perturbation velocities and
perturbation kinetic energy. BiGlobal stability (BiGSA) calculations are performed to assess the scopes and limitations of DS-LPE and BiGSA.
The flow over a porous laminated flat plate was investigated numerically and experimentally for various values of porosity of the lamination, φ, and flow Reynolds number, Re. The slip velocity at the fluid-porous interface, Uslip, the boundary layer thickness
over the porous lamination, δx, the shear stress at the interface, τslip, and the pressure gradient along the interface were examined to understand the flow characteristics at the fluid-porous interface. The flow was found to break down from a steady, uniform flow to an unsteady, non-uniform flow for certain values of Re at different φ, and this Re was termed as the breakdown Reynolds number, Reb. A Re − φ map distinguishing the flow regimes was derived based on these numerical and experimental results. The critical growth rates from BiGSA confirm the flow characterisation with ωi 0 for the steady,
uniform flow cases and ωi > 0 for the unsteady, non-uniform flow cases.
The influence of slip on the wake dynamics of flow past a square cylinder is studied numerically. The slip condition is derived from the Maxwell slip model in which the control parameter is the Knudsen number, Kn. We analyse two cases, (1) slip on leading
and trailing faces only and (2) slip on top and bottom faces only. The influence of slip is evaluated by calculating the Strouhal number, St. For case 1, it was found that slip has negligible influence on the wake dynamics. For case 2, it was found that slip stabilises the flow at lower Re by suppressing the onset of vortex shedding. A critical value of
Kn above which the vortex shedding is completely suppressed was determined for the lower Re. A Re − Kn phase space diagram was drawn based on the results of case 2, which demarcates the steady attached wake regime and the vortex shedding regimes of
the flow. The critical growth rates obtained from BiGSA were found to be positive for all cases at Kn Kn∗ and negative for Kn > Kn∗. The linear stability analysis using DS-LPE also show suppression of the perturbation growth at higher Kn. Hence, the results of DS-NS, DS-LPE and BiGSA are in close agreement, thereby confirming the stabilising nature of the slip surface on the flow.