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- Author or Editor: A. J. Bowen x
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Abstract
The authors first derive both Coriolis-induced and viscosity-induced stresses for arbitrary water depth and arbitrary wave direction. Opportunity is taken here to succinctly and rigorously derive the Longuet-Higgins virtual tangential stress due to wave motion. It is shown that the virtual stress is a projection on the surface slope of two viscous normal stresses acting on the vertical and horizontal planes. Then a simple Eulerian model is presented for the steady flow driven by waves and by waves and winds This simple Eulerian model demonstrates that the wave forcing can he easily incorporated with other conventional forcing, rather than resorting to a complicated and lengthy perturbation analysis of the Lagrangian equations of motion. A further focus is given to the wave-driven flow when the various limits of the wave-driven steady flow are discussed. The wave-driven steady flow given by the model yields a unified formula between Ursell and Hasselmann's inviscid but rotational theory and the Longuet-Higgins viscid but nonrotational theory, and it becomes an Eulerian counterpart of Madsen's deep-water solution when the deep-water limit is taken. The model is further expanded for the case of unsteady wave forcing, yielding a general formula for any type of time variation in the wave field. Two examples are considered: a suddenly imposed wave field that is then maintained steady and a suddenly imposed wave field that is then subject to internal and bottom frictional decay. The extension of these results to the case of random waves is briefly discussed. Finally, an example is presented that suggests the need to add surface wave forcing in classical shelf dynamics.
Abstract
The authors first derive both Coriolis-induced and viscosity-induced stresses for arbitrary water depth and arbitrary wave direction. Opportunity is taken here to succinctly and rigorously derive the Longuet-Higgins virtual tangential stress due to wave motion. It is shown that the virtual stress is a projection on the surface slope of two viscous normal stresses acting on the vertical and horizontal planes. Then a simple Eulerian model is presented for the steady flow driven by waves and by waves and winds This simple Eulerian model demonstrates that the wave forcing can he easily incorporated with other conventional forcing, rather than resorting to a complicated and lengthy perturbation analysis of the Lagrangian equations of motion. A further focus is given to the wave-driven flow when the various limits of the wave-driven steady flow are discussed. The wave-driven steady flow given by the model yields a unified formula between Ursell and Hasselmann's inviscid but rotational theory and the Longuet-Higgins viscid but nonrotational theory, and it becomes an Eulerian counterpart of Madsen's deep-water solution when the deep-water limit is taken. The model is further expanded for the case of unsteady wave forcing, yielding a general formula for any type of time variation in the wave field. Two examples are considered: a suddenly imposed wave field that is then maintained steady and a suddenly imposed wave field that is then subject to internal and bottom frictional decay. The extension of these results to the case of random waves is briefly discussed. Finally, an example is presented that suggests the need to add surface wave forcing in classical shelf dynamics.
Abstract
A model of forced, dissipative shore-oblique shallow water waves predicts net cross-shore infragravity wave propagation, in qualitative agreement with field observations. Forcing applied near the shore generates edge waves, whose energy is mostly trapped shoreward of the edge wave turning point. Forcing applied sufficiently far seaward of the turning point generates only evanescent waves, whose energy decays almost exponentially with distance from regions of forcing. Weakly dissipative edge waves are nearly cross-shore standing, whereas strongly dissipative edge waves propagate obliquely across-shore. Groups of directionally spread incident waves can nonlinearly force evanescent bound waves, which propagate shoreward, lowering the sea level under large incident waves. Unlike the bound waves described by previous researchers, evanescent bound waves are not released when incident waves break and do not radiate far from the breakpoint. Regions of evanescent waves between the shoreface and shore-parallel sandbars are barriers to energy transport, which can decouple bar- and shore-trapped waves even when dissipation is weak.
Abstract
A model of forced, dissipative shore-oblique shallow water waves predicts net cross-shore infragravity wave propagation, in qualitative agreement with field observations. Forcing applied near the shore generates edge waves, whose energy is mostly trapped shoreward of the edge wave turning point. Forcing applied sufficiently far seaward of the turning point generates only evanescent waves, whose energy decays almost exponentially with distance from regions of forcing. Weakly dissipative edge waves are nearly cross-shore standing, whereas strongly dissipative edge waves propagate obliquely across-shore. Groups of directionally spread incident waves can nonlinearly force evanescent bound waves, which propagate shoreward, lowering the sea level under large incident waves. Unlike the bound waves described by previous researchers, evanescent bound waves are not released when incident waves break and do not radiate far from the breakpoint. Regions of evanescent waves between the shoreface and shore-parallel sandbars are barriers to energy transport, which can decouple bar- and shore-trapped waves even when dissipation is weak.
Abstract
A model of forced, dissipative shore-oblique shallow water waves predicts net cross-shore infragravity wave propagation, in qualitative agreement with field observations. Forcing applied near the shore generates edge waves, whose energy is mostly trapped shoreward of the edge wave turning point. Forcing applied sufficiently far seaward of the turning point generates only evanescent waves, whose energy decays almost exponentially with distance from regions of forcing. Weakly dissipative edge waves are nearly cross-shore standing, whereas strongly dissipative edge waves propagate obliquely across-shore. Groups of directionally spread incident waves can nonlinearly force evanescent bound waves, which propagate shoreward, lowering the sea level under large incident waves. Unlike the bound waves described by previous researchers, evanescent bound waves are not released when incident waves break and do not radiate far from the breakpoint. Regions of evanescent waves between the shoreface and shore-parallel sandbars are barriers to energy transport, which can decouple bar- and shore-trapped waves even when dissipation is weak.
Abstract
A model of forced, dissipative shore-oblique shallow water waves predicts net cross-shore infragravity wave propagation, in qualitative agreement with field observations. Forcing applied near the shore generates edge waves, whose energy is mostly trapped shoreward of the edge wave turning point. Forcing applied sufficiently far seaward of the turning point generates only evanescent waves, whose energy decays almost exponentially with distance from regions of forcing. Weakly dissipative edge waves are nearly cross-shore standing, whereas strongly dissipative edge waves propagate obliquely across-shore. Groups of directionally spread incident waves can nonlinearly force evanescent bound waves, which propagate shoreward, lowering the sea level under large incident waves. Unlike the bound waves described by previous researchers, evanescent bound waves are not released when incident waves break and do not radiate far from the breakpoint. Regions of evanescent waves between the shoreface and shore-parallel sandbars are barriers to energy transport, which can decouple bar- and shore-trapped waves even when dissipation is weak.
Abstract
A set of moored, bottom-mounted and shipboard measurements, obtained in a straight section of the lower Hudson estuary during late summer and early fall of 1995, determine velocity, density, and along-channel pressure gradient throughout the 15-m water column, as well as providing direct eddy-correlation estimates of Reynolds stress and indirect inertial-range estimates of dissipation within 3 m of the bottom. The analysis focuses on testing 1) a simplified turbulent kinetic energy equation, in which production balances dissipation; 2) the Prandtl–Karman law of the wall, which is a relationship between bottom stress and near-bottom velocity gradient; and 3) a simplified depth-integrated along-channel momentum balance involving local acceleration, pressure gradient, and bottom stress. Estimates of production and dissipation agree well throughout the entire record. The relationship between bottom stress and velocity gradient is consistent with the law of the wall within approximately 1 m of the seafloor during flooding tides, but it departs from the law of the wall at greater heights during flooding tides and at all resolved heights during ebbing tides. The local stratification is too small to explain this effect, and the likely explanation is suppression of the turbulent length scale by the finite thickness of the relatively well-mixed layer beneath the pycnocline. Direct covariance estimates of bottom stress close the approximate momentum balance well during some periods, but are often smaller than the sum of the other terms in the balance by a factor of roughly up to 2. The agreement between stress estimates and the sum of the other terms is best during periods of strongest top-to-bottom stratification and worst during periods of weak stratification, for reasons that are not understood.
Abstract
A set of moored, bottom-mounted and shipboard measurements, obtained in a straight section of the lower Hudson estuary during late summer and early fall of 1995, determine velocity, density, and along-channel pressure gradient throughout the 15-m water column, as well as providing direct eddy-correlation estimates of Reynolds stress and indirect inertial-range estimates of dissipation within 3 m of the bottom. The analysis focuses on testing 1) a simplified turbulent kinetic energy equation, in which production balances dissipation; 2) the Prandtl–Karman law of the wall, which is a relationship between bottom stress and near-bottom velocity gradient; and 3) a simplified depth-integrated along-channel momentum balance involving local acceleration, pressure gradient, and bottom stress. Estimates of production and dissipation agree well throughout the entire record. The relationship between bottom stress and velocity gradient is consistent with the law of the wall within approximately 1 m of the seafloor during flooding tides, but it departs from the law of the wall at greater heights during flooding tides and at all resolved heights during ebbing tides. The local stratification is too small to explain this effect, and the likely explanation is suppression of the turbulent length scale by the finite thickness of the relatively well-mixed layer beneath the pycnocline. Direct covariance estimates of bottom stress close the approximate momentum balance well during some periods, but are often smaller than the sum of the other terms in the balance by a factor of roughly up to 2. The agreement between stress estimates and the sum of the other terms is best during periods of strongest top-to-bottom stratification and worst during periods of weak stratification, for reasons that are not understood.
