The shadowgraph method is used to visualize the convective flow in a water-filled square cavity, which is differentially heated and cooled from the opposing vertical sidewalls. Since in this system a quantitative recovery of the temperature field from the observed shadowgraph images is not possible, we apply a somewhat reverse procedure. The numerical solution of the cavity flow yields the field of the refractive index. By numerically integrating the path of light through this field, artificial shadowgraph images are constructed. This makes a comparison of the numerical and the experimental temperature fields possible and also leads to a clearer interpretation of the shadowgraph images and a better understanding of the way in which certain features are generated. The procedure is not restricted to the cavity flow, but can be applied whenever the field of the refractive index is available.
A non-parallel linear stability analysis which utilizes the assumptions
made in the
parabolized stability equations is applied to the buoyancy-driven flow
in a differentially
heated cavity. Numerical integration of the complete Navier–Stokes
and energy
equations is used to validate the non-parallel theory by introducing an
oscillatory
heat input at the upstream end of the boundary layer. In this way the stability
properties are obtained by analysing the evolution of the resulting
disturbances. The
solutions show that the spatial growth rate and wavenumber are highly dependent
on the transverse location and the disturbance flow quantity under consideration.
The local solution to the parabolized stability equations
accurately predicts the wave
properties observed in the direct simulation whereas conventional parallel
stability
analysis overpredicts the spatial amplification and the wavenumber.
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