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We investigate large time existence of solutions of theNavier-Stokes-Boussinesq equations with spatially almost periodic large datawhen the density stratification is sufficiently large. In 1996, Kimura andHerring \cite{KH} examined numerical simulations to show a stabilizing effectdue to the stratification. They observed scattered two-dimensionalpancake-shaped vortex patches lying almost in the horizontal plane. Our resultis a mathematical justification of the presence of such two-dimensionalpancakes. To show the existence of solutions for large times, we use$\ell^1$-norm of amplitudes. Existence for large times is then proven usingtechniques of fast singular oscillating limits and bootstrapping argument froma global-in-time unique solution of the system of limit equations.

Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data