Direct numerical simulation of transitional mixed convection flows: Viscous and inviscid instability mechanisms

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Receptivity studies using direct numerical simulation require computations of equilibrium flow and its response to deterministic excitation. Equivalent flow problem, without heat interaction for zero-pressure gradient boundary layer, has been studied with respect to wall-excitation by a finite difference high accuracy method based on the solution of Navier-Stokes equation in Sengupta and Bhaumik [Phys. Rev. Lett.107, 154501 (2011)] and Sengupta et al. [Phys. Rev. E85, 026308 (2012)]. One of the key features of this study has been that the same methodology is used for computing the equilibrium flow and the disturbance field. Computation of equilibrium flow was performed by solving Navier-Stokes equation to include the leading edge of the plate, so that the effects of leading edge singularity and the growth of the boundary layer is included in the nonlinear framework. When the same methodology is attempted for mixed convection flows past horizontal plate (with Boussinesq approximation to model heat transfer effects) some of the equilibrium flow features could not be explained with linear viscous instability theory results. For horizontal hot flat plate with adiabatic wall conditions, the equilibrium flow could be computed and its receptivity could be correlated with linear spatial theory for lower buoyancy parameter. Here, we focus on receptivity of mixed convection flows to wall excitation for the following cases which do not allow computing the equilibrium flows from the solution of Navier-Stokes equation: (i) Aadiabatic horizontal flat plate cooled significantly at the leading edge only and (ii) strongly heated isothermal wedge flow for a wedge angle of 60°. The cold plate case is particularly interesting as the linear spatial theory indicates enhanced stabilization for higher magnitude of the buoyancy parameter. Results presented for the cold plate case indicates disturbance growth outside the shear layer. This prompted us to re-investigate various mechanisms of instability present for mixed convection flows. There is no definitive study for inviscid mechanism in this respect and the present effort not only fills this void, but also explains the relative roles of viscous and inviscid mechanisms for strong heat transfer effects, within the Boussinesq approximation.