Cylinder wakes in shallow oscillatory flow: The coastal island wake problem

Research output: Contribution to journalArticle

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Abstract

Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the understanding of this complex flow phenomenon. Here, three-dimensional velocity field measurements of cylinder wakes in shallow-water oscillatory flow are conducted across a parameter space that is typical of tidal flow around shallow islands. The wake form in steady flows is typically described in terms of the stability parameter (where is the island diameter, is the water depth and is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan-Carpenter number (where is the tidal velocity amplitude and is the tidal period). In this study we demonstrate that when the influence of bottom friction is confined to a Stokes boundary layer the stability parameter is given by where is the ratio of the wavelength of the Stokes bottom boundary layer to the depth. Three classes of wake form are observed with decreasing wake stability: (i) steady bubble for ; (ii) unsteady bubble for ; and (iii) vortex shedding for . Transitions in wake form and wake stability are shown to depend on the magnitude and temporal evolution of the wake return flow. Scaling laws are developed to allow upscaling of the laboratory results to island wakes. Vertical and lateral transport depend on three parameters: (i) the flow aspect ratio ; (ii) the amplitude of tidal motion relative to the island size, given by ; and (iii) the relative influence of bottom friction to the flow depth, given by . A model of wake upwelling based on Ekman pumping from the bottom boundary layer demonstrates that upwelling in the near-wake region of an island scales with and is independent of the wake form. Finally, we demonstrate an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability.

Original languageEnglish
Pages (from-to)158-184
Number of pages27
JournalJournal of Fluid Mechanics
Volume874
DOIs
Publication statusPublished - 10 Sep 2019

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wakes
boundary layers
Boundary layers
upwelling water
Friction
pumping
friction
bubbles
near wakes
vortex shedding
water depth
steady flow
continental shelves
Scaling laws
Vortex shedding
tides
shallow water
Tides
shelves
Steady flow

Cite this

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title = "Cylinder wakes in shallow oscillatory flow: The coastal island wake problem",
abstract = "Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the understanding of this complex flow phenomenon. Here, three-dimensional velocity field measurements of cylinder wakes in shallow-water oscillatory flow are conducted across a parameter space that is typical of tidal flow around shallow islands. The wake form in steady flows is typically described in terms of the stability parameter (where is the island diameter, is the water depth and is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan-Carpenter number (where is the tidal velocity amplitude and is the tidal period). In this study we demonstrate that when the influence of bottom friction is confined to a Stokes boundary layer the stability parameter is given by where is the ratio of the wavelength of the Stokes bottom boundary layer to the depth. Three classes of wake form are observed with decreasing wake stability: (i) steady bubble for ; (ii) unsteady bubble for ; and (iii) vortex shedding for . Transitions in wake form and wake stability are shown to depend on the magnitude and temporal evolution of the wake return flow. Scaling laws are developed to allow upscaling of the laboratory results to island wakes. Vertical and lateral transport depend on three parameters: (i) the flow aspect ratio ; (ii) the amplitude of tidal motion relative to the island size, given by ; and (iii) the relative influence of bottom friction to the flow depth, given by . A model of wake upwelling based on Ekman pumping from the bottom boundary layer demonstrates that upwelling in the near-wake region of an island scales with and is independent of the wake form. Finally, we demonstrate an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability.",
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Cylinder wakes in shallow oscillatory flow : The coastal island wake problem. / Branson, Paul M.; Ghisalberti, Marco; Ivey, Gregory N.; Hopfinger, Emil J.

In: Journal of Fluid Mechanics, Vol. 874, 10.09.2019, p. 158-184.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Cylinder wakes in shallow oscillatory flow

T2 - The coastal island wake problem

AU - Branson, Paul M.

AU - Ghisalberti, Marco

AU - Ivey, Gregory N.

AU - Hopfinger, Emil J.

PY - 2019/9/10

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N2 - Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the understanding of this complex flow phenomenon. Here, three-dimensional velocity field measurements of cylinder wakes in shallow-water oscillatory flow are conducted across a parameter space that is typical of tidal flow around shallow islands. The wake form in steady flows is typically described in terms of the stability parameter (where is the island diameter, is the water depth and is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan-Carpenter number (where is the tidal velocity amplitude and is the tidal period). In this study we demonstrate that when the influence of bottom friction is confined to a Stokes boundary layer the stability parameter is given by where is the ratio of the wavelength of the Stokes bottom boundary layer to the depth. Three classes of wake form are observed with decreasing wake stability: (i) steady bubble for ; (ii) unsteady bubble for ; and (iii) vortex shedding for . Transitions in wake form and wake stability are shown to depend on the magnitude and temporal evolution of the wake return flow. Scaling laws are developed to allow upscaling of the laboratory results to island wakes. Vertical and lateral transport depend on three parameters: (i) the flow aspect ratio ; (ii) the amplitude of tidal motion relative to the island size, given by ; and (iii) the relative influence of bottom friction to the flow depth, given by . A model of wake upwelling based on Ekman pumping from the bottom boundary layer demonstrates that upwelling in the near-wake region of an island scales with and is independent of the wake form. Finally, we demonstrate an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability.

AB - Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the understanding of this complex flow phenomenon. Here, three-dimensional velocity field measurements of cylinder wakes in shallow-water oscillatory flow are conducted across a parameter space that is typical of tidal flow around shallow islands. The wake form in steady flows is typically described in terms of the stability parameter (where is the island diameter, is the water depth and is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan-Carpenter number (where is the tidal velocity amplitude and is the tidal period). In this study we demonstrate that when the influence of bottom friction is confined to a Stokes boundary layer the stability parameter is given by where is the ratio of the wavelength of the Stokes bottom boundary layer to the depth. Three classes of wake form are observed with decreasing wake stability: (i) steady bubble for ; (ii) unsteady bubble for ; and (iii) vortex shedding for . Transitions in wake form and wake stability are shown to depend on the magnitude and temporal evolution of the wake return flow. Scaling laws are developed to allow upscaling of the laboratory results to island wakes. Vertical and lateral transport depend on three parameters: (i) the flow aspect ratio ; (ii) the amplitude of tidal motion relative to the island size, given by ; and (iii) the relative influence of bottom friction to the flow depth, given by . A model of wake upwelling based on Ekman pumping from the bottom boundary layer demonstrates that upwelling in the near-wake region of an island scales with and is independent of the wake form. Finally, we demonstrate an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability.

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