Transport by waves and turbulence: Dilute suspensions in stably stratified plane Poiseuille flow

Suspended particle transport is inherent in a wide range of industrial and environmental flows, from energy generation to manufacturing and from marine to atmospheric systems. Such flows are inherently stratified where varying concentration of particulates changes the mean density of the fluid; however, the role of stratification on particle suspension is poorly understood. Here the suspension of sediments in a channel (plane Poiseuille) flow is resolved using numerical simulation where the flow is stably thermally stratified and the particles passive. This set up enables quantification of stratification controls sediment transport processes. Sediment suspension is resolved for settling velocities of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>V</a:mi> <a:mi>s</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>0.005</a:mn> </a:mrow> <a:mo>,</a:mo> <a:mo> </a:mo> <a:mrow> <a:msub> <a:mi>V</a:mi> <a:mi>s</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>0.01</a:mn> </a:mrow> </a:math> , and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>V</b:mi> <b:mi>s</b:mi> </b:msub> <b:mo>=</b:mo> <b:mn>0.02</b:mn> </b:mrow> </b:math> , made dimensionless by the friction velocity <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>u</c:mi> <c:mi>τ</c:mi> </c:msub> </c:math> . Our results show that stratification generates flow-scale mixing processes, which invalidate extant models of sediment suspension that have been used for over 100 years. For stratified flows, the dimensionless collapse of flow scalars and turbulent statistics is poor near the core of the channel, where large concentration gradients coincide with large-scale mixing events. Here the differences between vertical turbulent diffusivities of sediment and temperature increase with increasing <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>V</d:mi> <d:mi>s</d:mi> </d:msub> </d:math> , reaching <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>15</e:mn> <e:mspace width="0.16em"/> <e:mo>%</e:mo> </e:mrow> </e:math> for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>V</g:mi> <g:mi>s</g:mi> </g:msub> <g:mo>=</g:mo> <g:mn>0.02</g:mn> </g:mrow> </g:math> . Discrepancies arise due to a breakdown of the linear gradient diffusion hypothesis. Predictions using the gradient diffusion hypothesis are expected to worsen with increasing settling velocity, indicating that classical models poorly predict dilute particle transport in strongly stratified flows, which are common in a range of environmental and industrial settings. Further, in stratified flows a feedback loop is established that generates strong buoyancy forces in the core of the duct, having the profound impact of building a self-reinforcing two-layer sediment concentration profile. These results highlight that classical sediment transport models may underpredict the amount of turbulent mixing, and therefore the capability of flows to suspend material, where flow-scale mixing events occur. They further reveal mechanisms for the formation of a barrier to mixing which significantly reduces suspended load capacity in flows with an internal velocity maximum, such as ducts, pipes, gravity currents, and jets.