We show that low-order g-modes with large enough amplitudes to affect significantly the solar neutrino fluxes would produce surface velocities that are $10^4$ times larger than the observed upper limits and hence are ruled out by existing data. We also demonstrate that any large-amplitude, short-period oscillations that grow on a Kelvin-Helmholtz time scale will require, to affect solar neutrino fluxes, a large amount of energy (for g-modes, $10^9$ times the energy in the observed $p-$ mode oscillations) and a tiny amount of dissipation (for g-modes, $10^{-8}$ the dissipation rate of the $p$-modes).

10 pages, Institute for Advanced Study number AST 93/10