Quantification of Mixing Depth Using the Gradient Richardson Number in Submerged Aquatic Vegetation Meadows

Abstract

Upper layer thickness (mixing depth) is an essential parameter for estimating the dissolved inorganic carbon and carbon flux at the water surface based on their association with the vertical flux of dissolved inorganic carbon. Previous studies quantified the mixing depth without SAV meadow or penetration depth in the SAV meadow without stratification and wind stress. However, mixing depth related to interaction with submerged aquatic vegetations (SAVs), stratification, and wind stress has yet to be quantified in the previous studies. Our study is the first to quantify the theoretical mixing depth with SAVs according to wind stress, SAV height, and drag coefficient. Theoretical mixing depth was quantified from modeled vertical temperature profile, vertical profile of horizontal velocity, and gradient Richardson number (Ri_g,veg). We found that mixing depth at a Ri_g,veg of 100 demonstrated good agreement with numerical results on average, with the mixing depth estimated in this study (h_{U,this study}) showing high applicability to observations at Komuke Lagoon. Moreover, h_{U,this study} increased with the increasing wind stress and decreasing drag coefficient and SAV height. Further, we found that SAV meadows with stratification and wind stress could be divided into four hydrodynamic regimes: non-vegetated layers, upper vegetated layers, thermoclines, and benthic boundary layers. Our findings help us estimate mixing depth or vertical flux without complicated numerical simulation and understand flow interaction with SAV, wind stress, and stratification.