<p>Understanding hyporheic processes is key to support stream health and functioning. The present study addresses the impact of weak buoyancy effects on hyporheic exchange. In this context, we focus on the density-driven processes on pore scale, which had not been investigated so far to our knowledge. For that purpose, the transport of an active scalar across the interface between a turbulent free-flow region and a random sphere pack with macroscopically flat surface was investigated by pore-resolved single-domain direct numerical simulation. At a permeability Reynolds number of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11242_2025_2192_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(Re_K = 1.63\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>K</mi> </msub> <mo>=</mo> <mn>1.63</mn> </mrow> </math></EquationSource> </InlineEquation> and a friction Reynolds number of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11242_2025_2192_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(Re_\tau = 173\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>τ</mi> </msub> <mo>=</mo> <mn>173</mn> </mrow> </math></EquationSource> </InlineEquation>, seven simulation cases were evaluated with Rayleigh–Darcy numbers varying within the range of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11242_2025_2192_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="123" /> </InlineMediaObject> <EquationSource Format="TEX">\(Ra_\textrm{D} \in [-20, 400]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>a</mi> <mtext>D</mtext> </msub> <mo>∈</mo> <mrow> <mo stretchy="false">[</mo> <mo>-</mo> <mn>20</mn> <mo>,</mo> <mn>400</mn> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11242_2025_2192_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(Ra_\textrm{D} &lt; 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>a</mi> <mtext>D</mtext> </msub> <mo>&lt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> represents stabilising and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11242_2025_2192_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(Ra_\textrm{D} &gt; 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>a</mi> <mtext>D</mtext> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> destabilising buoyancy effects. While turbulent scalar transport dominates the well-mixed free-flow region, dispersive transport contributes considerably to the scalar flux within the sphere pack, even in the absence of buoyancy effects. The latter observation implies that the velocity and scalar field must be spatially heterogeneous. Under these conditions, even weak destabilising buoyancy effects can enhance spatial variations, strengthen preferred scalar advection paths, and increase the hyporheic flux. A stabilising stratification of the scalar field has the opposite effect and reduces the vertical exchange within the porous medium. We conclude that even though weak buoyancy effects do not introduce genuine density-driven instabilities, they have a clear quantitative impact on hyporheic exchange with far-reaching ecological implications.</p>

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Assessing the Impact of Weak Buoyancy Effects on Hyporheic Exchange: A Study by Pore-Resolved Direct Numerical Simulation

  • Simon v. Wenczowski,
  • Yoshiyuki Sakai,
  • Roser Casas-Mulet,
  • Gabriele Chiogna,
  • Juergen Geist,
  • Michael Manhart

摘要

Understanding hyporheic processes is key to support stream health and functioning. The present study addresses the impact of weak buoyancy effects on hyporheic exchange. In this context, we focus on the density-driven processes on pore scale, which had not been investigated so far to our knowledge. For that purpose, the transport of an active scalar across the interface between a turbulent free-flow region and a random sphere pack with macroscopically flat surface was investigated by pore-resolved single-domain direct numerical simulation. At a permeability Reynolds number of \(Re_K = 1.63\) R e K = 1.63 and a friction Reynolds number of \(Re_\tau = 173\) R e τ = 173 , seven simulation cases were evaluated with Rayleigh–Darcy numbers varying within the range of \(Ra_\textrm{D} \in [-20, 400]\) R a D [ - 20 , 400 ] , where \(Ra_\textrm{D} < 0\) R a D < 0 represents stabilising and \(Ra_\textrm{D} > 0\) R a D > 0 destabilising buoyancy effects. While turbulent scalar transport dominates the well-mixed free-flow region, dispersive transport contributes considerably to the scalar flux within the sphere pack, even in the absence of buoyancy effects. The latter observation implies that the velocity and scalar field must be spatially heterogeneous. Under these conditions, even weak destabilising buoyancy effects can enhance spatial variations, strengthen preferred scalar advection paths, and increase the hyporheic flux. A stabilising stratification of the scalar field has the opposite effect and reduces the vertical exchange within the porous medium. We conclude that even though weak buoyancy effects do not introduce genuine density-driven instabilities, they have a clear quantitative impact on hyporheic exchange with far-reaching ecological implications.