Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations

Turbulent mixing of water masses of different temperatures and salinities is an important process for both coastal and large-scale ocean circulation. It is, however, difficult to capture computationally. One of the reasons is that mixing in the ocean occurs at a wide range of complexity, with the Reynolds number reaching Re = O (10⁶), or even higher. In this study, we continue to investigate whether large eddy simulation (LES) can be a reliable computational tool for stratified mixing in turbulent oceanic flows. LES is attractive because it can be O (1000) times faster than a direct numerical simulation (DNS) of stratified mixing in turbulent flows. Before using the LES methodology to compute mixing in realistic oceanic flows, however, a careful assessment of the LES sensitivity with respect to Re needs to be performed first. The main objectives of this study are: (i) to investigate the performance of different LES models at high Re, such as those encountered in oceanic flows; and (ii) to study how mixing varies as a function of Re. To this end, as a benchmark we use the lock-exchange problem, which is described by unambigous and simple initial and boundary conditions. The background potential energy, which accurately quantifies irreversible mixing in an enclosed system, is used as the main criterion in a posteriori testing of LES. This study has two main achievements. The first is that we investigate the accuracy of six combinations of two different classes of LES models, namely eddy-viscosity and approximate deconvolution types, for 3 × 10³ ≤ Re ≤ 3 × 10⁴, for which DNS data is computed. We find that all LES models almost always provide significantly more accurate results than cases without LES models. Nevertheless, no single LES model that is persistently superior to others over this Re range could be identified. Then, an ensemble of the four best performing LES models is selected in order to estimate mixing taking place in this system at Re = 10⁵ and 10⁶, for which DNS is presently not feasible. Thus the second achievement of this study is to quantify mixing taking place in this system over an Re range that changes by three orders of magnitude. We find that the background potential energy increases by about 67% when Re is increased from Re = 10³ to Re = 10⁶, within the computation period, with the most significant increase taking place from Re = 3 × 10³ to Re = 10⁵.