A Karhunen-Loève based Galerkin approximation to Boussinesq equation Original Research Article

The Boussinesq equation which is derived from the Navier-Stokes equation is approximated by the amplitude equations constructed through the Karhunen-Loève (K-L) based Galerkin projection. The construction is worked out in a systematic way and some numerical experiments are performed. It is shown numerically that K-L based Galerkin approximation provides a satisfactory and robust description of the dynamics with an involvement of a relatively low degrees of freedom.