<p>This study examines whether the dispersion of passive particles at the free surface of a generic (nonturbulent) shallow flow can reliably represent the behavior of depth-keeping particles below the surface. A shallow configuration characterize many aquatic environments, such as coastal regions and lakes, where horizontal scales far exceed vertical ones, large-scale flow structures dominate, and observations are sometimes limited to the surface. We compare surface and subsurface horizontal velocities in both direction and magnitude, identifying distinct behaviors depending on the parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Re_F\delta ^2\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Re_F\)</EquationSource> </InlineEquation> is the Reynolds number based on forcing, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation> is the aspect ratio between the fluid layer depth and the horizontal forcing scale. At low <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Re_F\delta ^2\)</EquationSource> </InlineEquation>, deep flows match the surface flow in direction throughout the layer, but not in magnitude. At high <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(Re_F\delta ^2\)</EquationSource> </InlineEquation>, the magnitude matches (outside the bottom boundary layer), but not always the direction. Despite these differences, for all <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(Re_F\delta ^2\)</EquationSource> </InlineEquation>, surface particle patterns correlate with those in the upper quarter of the fluid layer. Filamentary structures caused by horizontal flow convergence remain spatially aligned within this region. Below it, at intermediate <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(Re_F\delta ^2\)</EquationSource> </InlineEquation>, deep filaments become diffuse and eventually vanish. At high <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(Re_F\delta ^2\)</EquationSource> </InlineEquation>, filaments persist at depth, but become spatially misaligned with surface filaments. These findings suggest that in shallow environments, surface observations can quantitatively infer subsurface transport processes in the upper quarter of the fluid layer. For the deeper part, knowledge of the vertical profiles of the mean flow yields insights into the horizontal transport processes.</p>

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Comparing surface and deep horizontal distributions of depth-keeping particles in shallow fluid layers

  • Lenin Moisés Flores Ramírez,
  • Matias Duran-Matute,
  • Herman J. H. Clercx

摘要

This study examines whether the dispersion of passive particles at the free surface of a generic (nonturbulent) shallow flow can reliably represent the behavior of depth-keeping particles below the surface. A shallow configuration characterize many aquatic environments, such as coastal regions and lakes, where horizontal scales far exceed vertical ones, large-scale flow structures dominate, and observations are sometimes limited to the surface. We compare surface and subsurface horizontal velocities in both direction and magnitude, identifying distinct behaviors depending on the parameter \(Re_F\delta ^2\) , where \(Re_F\) is the Reynolds number based on forcing, and \(\delta \) is the aspect ratio between the fluid layer depth and the horizontal forcing scale. At low \(Re_F\delta ^2\) , deep flows match the surface flow in direction throughout the layer, but not in magnitude. At high \(Re_F\delta ^2\) , the magnitude matches (outside the bottom boundary layer), but not always the direction. Despite these differences, for all \(Re_F\delta ^2\) , surface particle patterns correlate with those in the upper quarter of the fluid layer. Filamentary structures caused by horizontal flow convergence remain spatially aligned within this region. Below it, at intermediate \(Re_F\delta ^2\) , deep filaments become diffuse and eventually vanish. At high \(Re_F\delta ^2\) , filaments persist at depth, but become spatially misaligned with surface filaments. These findings suggest that in shallow environments, surface observations can quantitatively infer subsurface transport processes in the upper quarter of the fluid layer. For the deeper part, knowledge of the vertical profiles of the mean flow yields insights into the horizontal transport processes.