In stratified turbulence, the turbulence motion in the vertical direction is influenced by gravity. If the vertical density gradient is stable, the turbulence is suppressed, otherwise it is enhanced. Stratified turbulence occurs in most engineering applications involving buoyant jet discharges. For instance, dense effluents are often discharged into coastal waters using submerged outfalls in the form of inclined dense jets, whereby stable and unstable stratified turbulence exist simultaneously in the upper and lower region of the effluent trajectory, respectively. The assessment of the mixing characteristics of the inclined dense jet is essential for the design of the outfall configuration.

In terms of the trajectory, the inclined dense jet first rises up due to the discharge momentum until a maximum height is reached. Subsequently, the dense jet turns downward due to the negative buoyancy and impacts onto the seabed. Many experimental studies had been conducted on the inclined dense jet in the past to characterise the mixing characteristics (e.g. Shao and Law, 2010; Lai and Lee, 2012). More recently, several integral modeling studies (e.g. Palomar et al., 2012; Oliver et al., 2013) and computational fluid dynamics (CFD) studies (e.g. Vafeiadou et al., 2005; Oliver et al., 2008; Gildeh et al., 2015; Zhang et al., 2016) had also been performed for the assessment. These studies were typically carried out without the bottom wall boundary to facilitate the modelling computations. Thus, although useful results were obtained before the return point, they were not able to provide assessment of the bottom impact processes and the corresponding impact dilution, as well as the spreading along the seabed in the intermediate field.

In the present study, we performed a Large Eddy Simulations (LES) study to simulate 45° and 60° inclined dense jet in a stagnant ambient including the impact on the bottom wall boundary. The objective was to evaluate the performance of LES on the predictions of both the kinematic and mixing behavior of the inclined dense jet with bottom boundary in the near field region. For the LES simulations, the dynamic Smagorinsky sub-grid model was adopted, and accurate near wall modeling was employed to better reproduce the turbulence mixing at the impact point and in the spreading layer after the impact. The LES results were compared to the experimental measurements reported in the literature. Overall, we shall show that the LES simulations were able to better predict mixing behaviour of the inclined dense jet including the bottom impact processes than the k-ε model predictions. The dilution in the lower layer of the inclined dense jet was still somewhat under-predicted which was attributed to the buoyancy-induced instability.

The under-predictions pointed toward some shortcomings in the simulation of stratified turbulence mixing in this study. Turbulent energy spectrum can be broadly categorised into three ranges based on eddy sizes: energy-containing range, inertial sub-range and dissipation range. The basic assumption of LES is that the local grid spacing resides in the inertial sub-range where the turbulence motion can be represented by a isotropic sub-grid model. With stratified turbulence, however, the vertical turbulence motion may be influenced by the stratification within the grid spacing (Lindborg, 2006; Waite, 2011). One possible approach is to incorporate the deviated vertical motion directly into the LES subgird model to better represent the stratified turbulence motion within the grid itself (Cheng & Canuto, 1994). Another alternative is to further refine the grid spacing down to the critical resolution that is sufficiently small so that the stratification has little effect. To achieve this critical resolution, one needs to first examine the buoyancy scale L_b (Waite & Bartello, 2004). Khani and Waite (2014; 2015) found that the Smagorinsky model was significantly more costly among the tested models, the Kraichnan model was the least costly, and the dynamic Smagorinsky model was in between with a critical resolution of 0.24L_b for isotropic turbulence. These previous studies however mostly focused on stably stratified turbulence, the parallel criterion for unstably stratified turbulence remains unclear. It is thus essential to assess the critical resolution for unstably stratified engineering turbulence such as inclined dense jets in future work.

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