Resolving Small-scale Structures in Two-dimensional Boussinesq Convection by Spectral Methods with High Resolutions

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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.