Abstract
We have studied stably-stratified, fully-developed, turbulent channel flow by direct numerical simulation (DNS) and linear stability analysis. The DNS have been performed at higher Reynolds numbers (180 < Re_tau < 550), higher stratification levels (0 < Ri_tau < 960) and larger computational domains than previously existing simulations [1-2]. Two flow regimes have been observed depending on the level of stratification.
For low and moderate levels of stratification, internal gravity waves are confined within the central region of the channel while the flow close to the wall remains turbulent in a canonical way, presenting high- and low-speed streaks. This regime is consistent with previous simulations [1-2]. We have performed a linear stability analysis of this flow regime considering the mean velocity and density profiles from the DNS as base flow. We have employed a linear turbulence model to represent the energy dissipation and scalar diffusion felt at the large scales as a consequence of the small scales, similar to [3]. The results from this analysis indicate that those perturbations showing maximal transient growth correspond well with the waves in the center of the channel and with the streaks in the near wall region. In particular, the sizes and convection velocities of these structures are accurately predicted by the linear model.
For very strong stratification, a second regime has been observed in which the turbulence is suppressed in the core of the channel and the internal waves penetrate deeply in the wall-normal direction. These waves often reach the wall region, where the turbulence becomes patchy but can still be sustained. These patches can be very long and wide, requiring very large computational domains for their numerical simulation. This intermittent regime had not been reproduced by previous simulation studies in smaller computational domains, which reported flow laminarization at comparable stratification levels.
[1] V. Armenio and S. Sarkar. An investigation of stably stratified turbulent channel flow using large-eddy simulation. J. Fluid Mech., 459:1-42, 2002.
[2] O. Iida, N. Kasagi, and Y. Nagano. Direct numerical simulation of turbulent channel flow under stable density stratification. Int. J. Heat Mass Transfer, 45:1693-1703, 2002.
[3] W.C. Reynolds, W.C. and A.K.M.F. Hussain, The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments, 54:263-288, 1972.