Similarity theory based on the Dougherty-Ozmidov length scale

Abstract

Local similarity theory is suggested based on the Brunt-Vaisala frequency and the dissipation rate of turbulent kinetic energy instead the turbulent fluxes used in the traditional Monin-Obukhov similarity theory. Based on dimensional analysis (Pi theorem), it is shown that any properly scaled statistics of the small-scale turbulence are universal functions of a stability parameter defined as the ratio of a reference height z and the Dougherty-Ozmidov length scale which in the limit of z-less stratification is linearly proportional to the Obukhov length scale. Measurements of atmospheric turbulence made at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to examine the behaviour of different similarity functions in the stable boundary layer. It is found that in the framework of this approach the non-dimensional turbulent viscosity is equal to the gradient Richardson number whereas the non-dimensional turbulent thermal diffusivity is equal to the flux Richardson number. These results are a consequence of the approximate local balance between production of turbulence by the mean flow shear and viscous dissipation. The turbulence framework based on the Brunt-Vaisala frequency and the dissipation rate of turbulent kinetic energy may have practical advantages for estimating turbulence when the fluxes are not directly available.