scholarly journals The Hybrid Kelvin–Edge Wave and Its Role in Tidal Dynamics

2010 ◽  
Vol 40 (12) ◽  
pp. 2757-2767 ◽  
Author(s):  
Ziming Ke ◽  
Alexander E. Yankovsky
Keyword(s):  
Group Velocity ◽  
Wave Energy ◽  
Numerical Experiments ◽  
Tidal Energy ◽  
Ocean Modeling ◽  
Edge Wave ◽  
Kelvin Wave ◽  
Regional Ocean Modeling System ◽  
Offshore Wave ◽  
Zero Group

Abstract A full set of long waves trapped in the coastal ocean over a variable topography includes a zero (fundamental) mode propagating with the coast on its right (left) in the Northern (Southern) Hemisphere. This zero mode resembles a Kelvin wave at lower frequencies and an edge wave (Stokes mode) at higher frequencies. At the intermediate frequencies this mode becomes a hybrid Kelvin–edge wave (HKEW), as both rotational effects and the variable depth become important. Furthermore, the group velocity of this hybrid mode becomes very small or even zero depending on shelf width. It is found that in midlatitudes a zero group velocity occurs at semidiurnal (tidal) frequencies over wide (∼300 km), gently sloping shelves. This notion motivated numerical experiments using the Regional Ocean Modeling System in which the incident HKEW with a semidiurnal period propagates over a wide shelf and encounters a narrowing shelf so that the group velocity becomes zero at some alongshore location. The numerical experiments have demonstrated that the wave energy increases upstream of this location as a result of the energy flux convergence while farther downstream the wave amplitude is substantially reduced. Instead of propagating alongshore, the wave energy radiates offshore in the form of Poincaré modes. Thus, it is concluded that the shelf areas where the group velocity of the HKEW becomes zero are characterized by an increased tidal amplitude and (consequently) high tidal energy dissipation, and by offshore wave energy radiation. This behavior is qualitatively consistent with the dynamics of semidiurnal tides on wide shelves narrowing in the direction of tidal wave propagation, including the Patagonia shelf and the South China Sea.

Combined Effects of Wind-Driven Upwelling and Internal Tide on the Continental Shelf

2010 ◽  
Vol 40 (4) ◽  
pp. 737-756 ◽  
Author(s):  
A. L. Kurapov ◽  
J. S. Allen ◽  
G. D. Egbert
Keyword(s):  
Continental Shelf ◽  
Internal Tide ◽  
Tidal Energy ◽  
Horizontal Velocity ◽  
Internal Tides ◽  
Ocean Modeling ◽  
Vertical Shear ◽  
Momentum Balance ◽  
Surface Boundary ◽  
Regional Ocean Modeling System

Abstract Internal tides on the continental shelf can be intermittent as a result of changing hydrographic conditions associated with wind-driven upwelling. In turn, the internal tide can affect transports associated with upwelling. To study these processes, simulations in an idealized, alongshore uniform setup are performed utilizing the hydrostatic Regional Ocean Modeling System (ROMS) with conditions corresponding, as closely as possible, to the central Oregon shelf. “Wind only” (WO), “tide only” (TO), and “tide and wind” (TW) solutions are compared, utilizing cases with constant upwelling-favorable wind stress as well as with time-variable observed stress. The tide is forced by applying cross-shore barotropic flow at the offshore boundary with intensity sufficient to generate an internal tide with horizontal velocity amplitudes near 0.15 m s−1, corresponding to observed levels. The internal tide affects the subinertial circulation, mostly through the changes in the bottom boundary layer variability, resulting in a larger bottom stress and a weaker depth-averaged alongshore current in the TW case compared to WO. The spatial variability of the cross-shore and vertical volume transport is also affected. Divergence in the Reynolds stress associated with the baroclinic tidal flow contributes to the tidally averaged cross-shore momentum balance. Internal waves cause high-frequency variability in the turbulent kinetic energy in both the bottom and surface boundary layers, causing periodic restratification of the inner shelf in the area of the upwelling front. Increased vertical shear in the horizontal velocity resulting from the superposition of the upwelling jet and the internal tide results in intermittent patches of intensified turbulence in the mid–water column. Variability in stratification associated with upwelling can affect not only the propagation of the internal tide on the shelf, but also the barotropic-to-baroclinic energy conversion on the continental slope, in this case changing the classification of the slope from nearly critical to supercritical such that less barotropic tidal energy is converted to baroclinic and a larger fraction of the baroclinic energy is radiated into the open ocean.

scholarly journals The Evolution of a Buoyant River Plume in Response to a Pulse of High Discharge from a Small Midlatitude River

2020 ◽  
Vol 50 (7) ◽  
pp. 1915-1935
Author(s):  
Emily Lemagie ◽  
James Lerczak
Keyword(s):  
Pulse Duration ◽  
River Mouth ◽  
Coastal Ocean ◽  
Ocean Modeling ◽  
Rain Event ◽  
Kelvin Wave ◽  
Regional Ocean Modeling System ◽  
Transport Pathways ◽  
Freshwater Transport ◽  
The Impact

AbstractA unique feature of small mountainous rivers is that discharge can be elevated by an order of magnitude during a large rain event. The impact of time-varying discharge on freshwater transport pathways and alongshore propagation rates in the coastal ocean is not well understood. A suite of simulations in an idealized coastal ocean domain using the Regional Ocean Modeling System (ROMS) with varying steady background discharge conditions (25–100 m3 s−1), pulse amplitude (200–800 m3 s−1), pulse duration (1–6 days), and steady downwelling-favorable winds (0–4 m s−1) are compared to investigate the downstream freshwater transport along the coast (in the direction of Kelvin wave propagation) following a discharge pulse from the river. The nose of the pulse propagates rapidly alongshore at 0.04–0.32 m s−1 (faster propagation corresponds with larger pulse volume and faster winds) transporting 13%–66% of the discharge. The remainder of the discharge volume initially accumulates in the bulge near the river mouth, with lower retention for longer pulse duration and stronger winds. Following the pulse, the bulge eddy disconnects from the river mouth and is advected downstream at 0–0.1 m s−1, equal to the depth-averaged wind-driven ambient water velocity. As it transits alongshore, it sheds freshwater volume farther downstream and the alongshore freshwater transport stays elevated between the nose and the transient bulge eddy. The evolution of freshwater transport at a plume cross section can be described by the background discharge, the passage of the pulse nose, and a slow exponential return to background conditions.

Spatial and Temporal Variability of the M2 Internal Tide Generation and Propagation on the Oregon Shelf

2011 ◽  
Vol 41 (11) ◽  
pp. 2037-2062 ◽  
Author(s):  
J. J. Osborne ◽  
A. L. Kurapov ◽  
G. D. Egbert ◽  
P. M. Kosro
Keyword(s):  
Spatial Variability ◽  
Hot Spot ◽  
Time Windows ◽  
Internal Tide ◽  
Tidal Energy ◽  
Horizontal Resolution ◽  
Ocean Modeling ◽  
Spatial And Temporal Variability ◽  
Affect Intensity ◽  
Regional Ocean Modeling System

Abstract A 1-km-horizontal-resolution model based on the Regional Ocean Modeling System is implemented along the Oregon coast to study average characteristics and intermittency of the M2 internal tide during summer upwelling. Wind-driven and tidally driven flows are simulated in combination, using realistic bathymetry, atmospheric forcing, and boundary conditions. The study period is April through August 2002, when mooring velocities are available for comparison. Modeled subtidal and tidal variability on the shelf are in good quantitative agreement with moored velocity time series observations. Depth-integrated baroclinic tidal energy flux (EF), its divergence, and topographic energy conversion (TEC) from the barotropic to baroclinic tide are computed from high-pass-filtered, harmonically analyzed model results in a series of 16-day time windows. Model results reveal several “hot spots” of intensive TEC on the slope. At these locations, TEC is well balanced by EF divergence. Changes in background stratification and currents associated with wind-driven upwelling and downwelling do not appreciably affect TEC hot spot locations but may affect intensity of internal tide generation at those locations. Relatively little internal tide is generated on the shelf. Areas of supercritical slope near the shelf break partially reflect baroclinic tidal energy to deeper water, contributing to spatial variability in seasonally averaged on-shelf EF. Despite significant temporal and spatial variability in the internal tide, the alongshore-integrated flux of internal tide energy onto the Oregon shelf, where it is dissipated, does not vary much with time. Approximately 65% of the M2 baroclinic tidal energy generated on the slope is dissipated there, and the rest is radiated toward the shelf and interior ocean in roughly equal proportions. An experiment with smoother bathymetry reveals that slope-integrated TEC is more sensitive to bathymetric roughness than on-shelf EF.

Double Kelvin waves with continuous depth profiles

1968 ◽  
Vol 34 (1) ◽  
pp. 49-80 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Group Velocity ◽  
Transition Zone ◽  
Kelvin Wave ◽  
Trapped Modes ◽  
Full Account ◽  
Higher Modes ◽  
Depth Profiles ◽  
Different Depths ◽  
Bounded Below ◽  
Asymptotic Forms

The possibility of long waves in a rotating ocean being trapped along a straight discontinuity in depth was demonstrated in a recent paper (Longuet-Higgins 1968). The analysis is now extended to the situation where the depth varies continuously, in a zone separating two regions of different depths. The trapping of waves in the transition zone is investigated, taking full account of the horizontal divergence of the motion.If the profile of the depth is assumed to be monotonic, then it is shown that the trapped waves always travel along the transition zone with the shallower water to their right in the northern hemisphere and to their left in the southern hemisphere. The wave period must always exceed a pendulum-day. The period is also bounded below by a quantity depending inversely on the maximum bottom gradient.By allowing the width W of the transition zone to vary, asymptotic forms for the trapped modes are obtained, both as W → 0 and as W → ∞. In the limit as W → 0 the depth becomes discontinuous, and it is shown that the lowest mode then becomes a double Kelvin wave (Longuet-Higgins 1968) propagated along the discontinuity. The periods of the higher modes, on the other hand, all tend to infinity; these modes become steady currents.Numerical calculations of the trapped modes are presented for two different laws of depth in the transition zone. It is found that as W → 0 the lowest mode is insensitive to the form of the depth profile. Higher modes depend on the details of the profile. Hence the lowest mode is the most likely to be observed in the real ocean.The dispersion relation is also investigated. It is shown that the group-velocity of all modes must change sign at some point in the range of wave-numbers, if the divergence is taken into account. When the divergence was neglected the lowest mode appeared to be exceptional, in that the group-velocity was always in the same direction. This anomaly is now removed.

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