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Instability of Viscoelastic Fluids in Nearly Parallel Flows: a Pseudo-Spectral Analysis

In the present work, the effect of fluidʹs elasticity was investigated on the hydrodynamic instability of Blasius flow. To determine the critical Reynolds number as a function of the elasticity number, a two-dimensional linear temporal stability analysis was invoked. The viscoelastic fluid is assumed to obey the Waltersʹ B fluid model for which base flow velocity profiles were fortunately available from literature. Neglecting terms nonlinear in the perturbation quantities, a Generalized Orr-Sommerfeld equation was obtained incorporating an elastic term. The eigenvalue problem so obtained was solved numerically using the Chebychev collocation-point method. Based on the results obtained in this work, fluidʹs elasticity is predicted to have a destabilizing effect on the Blasius flow.