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

Two-dimensional Boussinesq convection is studied numerically with very fine spatial resolutions up to 4096^2. 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 (T_c). Our study shows that the vorticity will blow up at a finite time with |\omega|_{max} \~{(T_c-t)}^{-1.61} and |\nabla \theta|_{max} ~ {(T_c - t)}^{-3.58}.