Divergent-rotational modes and passive scalars in stratified turbulence
Seminar Room 1, Newton Institute
AbstractStrongly stratified turbulent flows are anisotropic but have three-dimensional dynamics with a forward energy cascade as shown by Lindborg (2006). Simulations with hyperviscosity also revealed an inertial range with a horizontal k^-5/3-spectrum. We have continued this work and examined the features of divergent and rotational modes, and of passive scalars in the inertial range of stratified turbulence.
The Helmholtz decomposition of the velocity into a rotational and divergent part have been used to study vortices and internal waves in stratified flows. In flows with mainly vertically oriented vortices the rotational part dominates while the divergent part dominates when there are mainly internal waves. The timescale ratio of the 'fast' waves and the 'slow' horizontal vortical motions can be estimated as the vertical Froude number F_v = u/Nl_v, where u is a horizontal velocity scale, l_v a verti cal length scale, N the Brunt-Vaisala frequency. It is often assumed that F_v = 0 in strongly stratified flows suggesting separate time scales of vortices and waves, and consequently weak interactions. However, scaling analysis suggests l_v = u/N in stratified turbulence, i.e. F_v = 1, which was supported by DNS (Brethouwer et al. 2007). In stratified turbulence the divergent and rotational modes may thus have similar timescales leading to strong nonlinear interactions between rotational and dive rgent modes. This implies that forcing in either divergent or rotational modes may have minor effects on the inertial range dynamics of stratified turbulence. Results of simulations with different stratification and resolution show that the energy of divergent and rotational modes hav e the same magnitude in the inertial range when large-scale rotational modes are forced, see Lindborg & Brethouwer (2007). In the simulations with forcing of divergent modes, small horizontal wave numbers and one vertical wave number are forced which introduces a vertical length scale. Results show that the inertial range spectra are very similar in simulations with forcing of rotational modes and divergent modes, suggesting similar dynamics, if in the latter simulations the large-scale dynamics o beys F_v = 1, but deviations are found when this condition is not fulfilled. The next subject is a passive scalar in stratified turbulence. The Obukhov-Corrsin theory for the one-dimensional spectrum of the variance of a passive scalar in the Kolmogorov inertial range of turbulence predicts a k^-5/3 slope. The second-order structure function according to the same theory has a r^2/3 power-law range. Measurements of horizontal spectra and structure functions of passive scalars (e.g. ozone) in the mesoscale range of the middle atmosphere are consistent with this theory. This is remarkable because the mesoscale range is strongly stratified and does not resemble Kolmogorov turbulence. We have carried out numerical simulations of stratified turbulence with large-scale forcing, hyperviscosity