Resolving Small-scale Structures in Two-dimensional Boussinesq Convection by Spectral Methods with High Resolutions
Abstract
Two-dimensional Boussinesq convection is studied numerically with very fine spatial resolutions up to 40962. Our numerical study starts with a smooth asymmetric initial condition, which is chosen to make the flow field well confined in the computational domain until the blow-up time (Tc). Our study shows that the vorticity will blow up at a finite time with |ω|max \~(Tc-t)-1.61 and |∇ θ|max ~ (Tc - t)-3.58.
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