Stratified turbulence: a possible interpretation of some geophysical turbulence measurements

For stably-stratified regions of both the atmosphere and the oceans, several existing sets of smaller-scale data, with horizontal length scales ranging from the Ozmidov scale $\ell_o = \sqrt{\epsilon/N^3}$ to several hundred times $\ell_o$, appear to display Kolmogorov-Obukov-Corrsin inertial ranges in horizontal spectra. For both the atmospheric and oceanic data, this corresponds to horizontal length scales of roughly 1 to at least several hundred meters. Based upon results from numerical simulations$^{1,3}$ and theoretical arguments$^{1,2}$ it is argued that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence$^{4}$ explain these data. In stratified turbulence a strong downscale transfer of energy exists in the horizontal, and with this the development of a horizontal (but not vertical) spectral inertial range above $\ell_o$. This downscale transfer of energy can then lead to smaller-scale instabilities and turbulence, providing new `pathways' to turbulence in geophysical flows. $^1$E.Lindborg,2005,{\it Geophys.Res.Ltrs.},{\bf 32},L01809. \\ $^2$E.Lindborg,2006,{\it J.Fluid Mech.},{\bf 550},207. \\ $^3$J.J.Riley,S.M.deBruynKops,2003,{\it Phys.Fluids},{\bf 15},2047. \\ $^4$D.K.Lilly, 1983,{\it J.Atmos.Sci.},{\bf 40},749.