Turbulent Mixing in the benthic biolayer of streams with bedforms
Authors: Monofy Ahmed Mostafa Ibrahem Mostafa , Grant Stanley 
Published: March 2020

&lt;p&gt;The importance of the benthic biolayer (the first few centimeters in the shallow part of the streambed) comes from the active biogeochemical reactions that happen within this thin layer. Currently, many studies use the simplified approach of using the constant profile to represent the diffusivity in the sedimented; however, other studies claim that the exponential profile is a better representation due to the turbulence penetration into the sediment bed. In this work, we are using an analytical model to simulate the temporal variation of solute concentration in water column in bedform morphology type by adopting two diffusivity profile; constant diffusivity profile, and exponential diffusivity profile. This rigorous analytical framework was built by Grant et al. 2019 (not published yet),&amp;#160; and is based on Duhamel&amp;#8217;s Theorem. The model is used to fit a set of laboratory data that were performed on streams with dunes type bedforms, where temporal concentration variation is measured in the water column. Based on Root Mean Square Error (RMSE), coefficient of determination (R&lt;sup&gt;2&lt;/sup&gt;), and modified Akaike Information Criterion (AICc), the exponential profile is superior over the whole range of Permeability Reynolds Number, and it can be considered as the best fit for the laboratory data compared to the constant diffusivity. &amp;#160;Additionally, the influence of sediment bed depth on the effective diffusivity, and therefore, on the benthic biolayer characteristics is investigated here by running the model with constant diffusivity profile in Infinite and finite sediment bed cases. An indicator () to determine whether the sediment bed depth influences the diffusivity within the sediment domain or not, is introduced here. when this indicator is larger than 1, the sediment bed depth will likely influence the diffusivity within the sediment. Based on our results, our analytical framework can be a predictive tool for the solute transfer into the benthic layer in bedform morphology type.&lt;/p&gt;&lt;p&gt;&lt;img 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&quot; alt=&quot;&quot;&gt;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;