• Bühler, O., 2009: Waves and Mean Flows. 2nd ed. Cambridge University Press, 374 pp., https://doi.org/10.1017/CBO9781107478701.

  • Burchard, H., R. D. Hetland, E. Schulz, and H. M. Schuttelaars, 2011: Drivers of residual estuarine circulation in tidally energetic estuaries: Straight and irrotational channels with parabolic cross section. J. Phys. Oceanogr., 41, 548570, https://doi.org/10.1175/2010JPO4453.1.

    • Search Google Scholar
    • Export Citation
  • Cohen, J. H., A. M. Internicola, R. A. Mason, and T. Kukulka, 2019: Observations and simulations of microplastic debris in a tide, wind, and freshwater-driven estuarine environment: The Delaware Bay. Environ. Sci. Technol., 53, 14 20414 211, https://doi.org/10.1021/acs.est.9b04814.

    • Search Google Scholar
    • Export Citation
  • Feng, S., R. T. Cheng, and X. Pangen, 1986: On tide-induced Lagrangian residual current and residual transport: 1. Lagrangian residual current. Water Resour. Res., 22, 16231634, https://doi.org/10.1029/WR022i012p01623.

    • Search Google Scholar
    • Export Citation
  • Garrett, C., 2004: Lecture 8: Tidal rectification and stokes drift. Woods Hole Oceanographic Institution Geophysical Fluid Dynamics Annual Proceedings, Vol. 2004, Woods Hole Oceanographic Institution, 104110, https://gfd.whoi.edu/gfd-publications/gfd-proceedings-volumes/2004-2/.

  • Jay, D. A., 1991: Estuarine salt conservation: A Lagrangian approach. Estuarine Coastal Shelf Sci., 32, 547565, https://doi.org/10.1016/0272-7714(91)90074-L.

    • Search Google Scholar
    • Export Citation
  • Jay, D. A., and J. D. Musiak, 1994: Particle trapping in estuarine tidal flows. J. Geophys. Res., 99, 20 44520 461, https://doi.org/10.1029/94JC00971.

    • Search Google Scholar
    • Export Citation
  • Kennish, M. J., 2002: Environmental threats and environmental future of estuaries. Environ. Conserv., 29, 78107, https://doi.org/10.1017/S0376892902000061.

    • Search Google Scholar
    • Export Citation
  • LeBlond, P. H., 1978: On tidal propagation in shallow rivers. J. Geophys. Res., 83, 47174721, https://doi.org/10.1029/JC083iC09p04717.

    • Search Google Scholar
    • Export Citation
  • Lemagie, E. P., and J. A. Lerczak, 2015: A comparison of bulk estuarine turnover timescales to particle tracking timescales using a model of the Yaquina Bay estuary. Estuaries Coasts, 38, 17971814, https://doi.org/10.1007/s12237-014-9915-1.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., and W. R. Geyer, 2004: Modeling the lateral circulation in straight, stratified estuaries. J. Phys. Oceanogr., 34, 14101428, https://doi.org/10.1175/1520-0485(2004)034<1410:MTLCIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Li, C., and J. O’Donnell, 1997: Tidally driven residual circulation in shallow estuaries with lateral depth variation. J. Geophys. Res., 102, 27 91527 929, https://doi.org/10.1029/97JC02330.

    • Search Google Scholar
    • Export Citation
  • Li, M., P. Cheng, R. Chant, A. Valle-Levinson, and K. Arnott, 2014: Analysis of vortex dynamics of lateral circulation in a straight tidal estuary. J. Phys. Oceanogr., 44, 27792795, https://doi.org/10.1175/JPO-D-13-0212.1.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M., 1969: On the transport of mass by time-varying ocean currents. Deep-Sea Res. Oceanogr. Abstr., 16, 431447, https://doi.org/10.1016/0011-7471(69)90031-X.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., and W. R. Geyer, 2010: Advances in estuarine physics. Annu. Rev. Mar. Sci., 2, 3558, https://doi.org/10.1146/annurev-marine-120308-081015.

    • Search Google Scholar
    • Export Citation
  • Nunes, R., and J. Simpson, 1985: Axial convergence in a well-mixed estuary. Estuarine Coastal Shelf Sci., 20, 637649, https://doi.org/10.1016/0272-7714(85)90112-X.

    • Search Google Scholar
    • Export Citation
  • Ridderinkhof, H., and J. Zimmerman, 1992: Chaotic stirring in a tidal system. Science, 258, 11071111, https://doi.org/10.1126/science.258.5085.1107.

    • Search Google Scholar
    • Export Citation
  • Valle-Levinson, A., 2008: Density-driven exchange flow in terms of the Kelvin and Ekman numbers. J. Geophys. Res., 113, C04001, https://doi.org/10.1029/2007JC004144.

    • Search Google Scholar
    • Export Citation
  • Zimmerman, J., 1979: On the Euler-Lagrange transformation and the Stokes’ drift in the presence of oscillatory and residual currents. Deep-Sea Res, 26A, 505520, https://doi.org/10.1016/0198-0149(79)90093-1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 519 519 44
Full Text Views 168 168 7
PDF Downloads 215 215 11

Surface Convergence Zones due to Lagrangian Residual Flow in Tidally Driven Estuaries

Tobias KukulkaaUniversity of Delaware, Newark, Delaware

Search for other papers by Tobias Kukulka in
Current site
Google Scholar
PubMed
Close
and
Robert J. ChantbRutgers University, New Brunswick, New Jersey

Search for other papers by Robert J. Chant in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Buoyant material, such as floating debris, marine organisms, and spilled oil, is aggregated and trapped within estuaries. Traditionally, the aggregation of buoyant material is assumed to be a consequence of converging Eulerian surface currents, often associated with lateral (cross-estuary) density gradients that drive baroclinic lateral circulations. This study explores an alternative aggregation mechanism due to tidally driven Lagrangian residual circulations without Eulerian convergence zones and without lateral density variation. In a tidally driven estuary, the depth-dependent tidal phase of the lateral velocity varies across the estuary. This study demonstrates that the lateral movement of surface trapped material follows the tidal phase, resulting in a lateral Lagrangian residual circulation known as Stokes drift for small-amplitude motions. For steeper bathymetry, the lateral change in tidal phase is greater and the corresponding lateral Lagrangian residual flow faster. At local depth extrema, e.g., in the thalweg, depth does not vary laterally, so that the associated tidal phase is laterally constant. Therefore, the Stokes drift is weak near depth extrema resulting in Lagrangian convergence zones where buoyant material concentrates. These ideas are evaluated employing an idealized analytic model in which the along-estuary tidal flow is driven by an imposed barotropic pressure gradient, whereas cross-estuary flow is induced by the Coriolis force. Model results highlight that convergence zones due to Lagrangian residual velocities are efficient in forming persistent aggregation regions of buoyant material along the estuary.

Significance Statement

Our study focuses on the aggregation of buoyant material (e.g., debris, oil, organisms) in estuaries. Traditionally, the aggregation of buoyant material is assumed to be a consequence of converging Eulerian surface currents, often associated with lateral (cross-estuary) density gradients that drive baroclinic lateral circulations. Our study explores an alternative aggregation mechanism due to tidally driven Lagrangian residual circulations without Eulerian convergence zones and without lateral density variation. Our results highlight that convergence zones due to Lagrangian residual velocities are efficient in forming persistent aggregation regions of buoyant material along the estuary.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tobias Kukulka, kukulka@udel.edu

Abstract

Buoyant material, such as floating debris, marine organisms, and spilled oil, is aggregated and trapped within estuaries. Traditionally, the aggregation of buoyant material is assumed to be a consequence of converging Eulerian surface currents, often associated with lateral (cross-estuary) density gradients that drive baroclinic lateral circulations. This study explores an alternative aggregation mechanism due to tidally driven Lagrangian residual circulations without Eulerian convergence zones and without lateral density variation. In a tidally driven estuary, the depth-dependent tidal phase of the lateral velocity varies across the estuary. This study demonstrates that the lateral movement of surface trapped material follows the tidal phase, resulting in a lateral Lagrangian residual circulation known as Stokes drift for small-amplitude motions. For steeper bathymetry, the lateral change in tidal phase is greater and the corresponding lateral Lagrangian residual flow faster. At local depth extrema, e.g., in the thalweg, depth does not vary laterally, so that the associated tidal phase is laterally constant. Therefore, the Stokes drift is weak near depth extrema resulting in Lagrangian convergence zones where buoyant material concentrates. These ideas are evaluated employing an idealized analytic model in which the along-estuary tidal flow is driven by an imposed barotropic pressure gradient, whereas cross-estuary flow is induced by the Coriolis force. Model results highlight that convergence zones due to Lagrangian residual velocities are efficient in forming persistent aggregation regions of buoyant material along the estuary.

Significance Statement

Our study focuses on the aggregation of buoyant material (e.g., debris, oil, organisms) in estuaries. Traditionally, the aggregation of buoyant material is assumed to be a consequence of converging Eulerian surface currents, often associated with lateral (cross-estuary) density gradients that drive baroclinic lateral circulations. Our study explores an alternative aggregation mechanism due to tidally driven Lagrangian residual circulations without Eulerian convergence zones and without lateral density variation. Our results highlight that convergence zones due to Lagrangian residual velocities are efficient in forming persistent aggregation regions of buoyant material along the estuary.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tobias Kukulka, kukulka@udel.edu
Save