Stokes Drift in Topographic Waves over an Enclosed Basin Shelf

AbstractThe effect of the continental shelf wave on the flow field over the southern shelf of the Caspian Sea (CS) as the largest enclosed basin of the world, is investigated. Considerable currents with subinertial time scales are observed over the continental shelf in the southern CS. For variations in the surface layer with typical periods of 1 day, local episodic wind events appear to be the driving force. For longer time scales, it is suggested that the observed currents are due to passing continental shelf waves. Measurements over the continental shelf and shelf slope, showing periods of 2–6 days, indicate the presence of such waves. Combined with theory and numerical modeling, the amplitude of the continental shelf wave modes at the coast is assessed from current meter observations. It is demonstrated that the mean drift velocity (the Stokes drift) for long continental shelf waves is determined entirely by the shelf geometry. For the actual shelf mode, it is shown that the associated Stokes drift constitute a nonnegligible mean current along the shelf. This current should be taken into account when assessing the transport of biological material and neutral tracers along the southern coast of the CS.

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The stability of continental shelf waves I. Side band instability and long wave resonance

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000001417 ◽

1977 ◽

Vol 20 (1) ◽

pp. 13-30 ◽

Cited By ~ 7

Author(s):

R. Grimshaw

Keyword(s):

Continental Shelf ◽

Stability Criterion ◽

Wave Speed ◽

Side Band ◽

Long Wave ◽

Wave Resonance ◽

Shelf Wave ◽

Shelf Waves ◽

The Stability ◽

Continental Shelf Waves

AbstractContinental shelf waves are examined for side band instability. It is shown that a modulated shelf wave is described by a nonlinear Schrödinger equation, from which the stability criterion is derived. Long shelf waves are stable to side band modulations, but as the wavenumber is increased there are regions of instability (in wavenumber space). A change of stability occurs at each long wave resonance, defined by the condition that the group velocity of the shelf wave equals a long wave speed. Equations describing the long wave resonance are derived.

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Continental Shelf Wave Propagation in the Mid-Atlantic Bight: A General Dispersion Relation

Journal of Physical Oceanography ◽

10.1175/jpo-d-11-098.1 ◽

2012 ◽

Vol 42 (4) ◽

pp. 558-568 ◽

Cited By ~ 14

Author(s):

William J. Schulz ◽

Richard P. Mied ◽

Charlotte M. Snow

Keyword(s):

Continental Shelf ◽

Sea Surface ◽

Long Wave ◽

Mode Dispersion ◽

Shelf Wave ◽

General Dispersion ◽

Shelf Waves ◽

Long Wave Approximation ◽

Continental Shelf Waves ◽

Good Agreement

Abstract The authors address the propagation of continental shelf waves in the Mid-Atlantic Bight. An analytical model of the bathymetry in the region is constructed by representing the continental shelf as a gently sloping bottom, which deepens linearly with offshore distance to the place where it meets the continental slope. Seaward of that point, the bathymetry is modeled with an exponentially decaying function of distance. The linearized, barotropic equations of hydrostatic motion, subject to the long-wave approximation, yield separate shelf and slope solutions, which are matched at the shelf break to specify the eigenfunctions. The associated eigenvalues define the dispersion relations for each of the modes. Wavenumber–frequency pairs derived from NOAA sea surface height stations along the coast are plotted on the first-mode dispersion curve, and the agreement is good. The theory also shows good agreement with the wave data of D. P. Wang.

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Localised continental shelf waves: geometric effects and resonant forcing

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.588 ◽

2015 ◽

Vol 785 ◽

pp. 54-77 ◽

Cited By ~ 3

Author(s):

J. T. Rodney ◽

E. R. Johnson

Keyword(s):

Continental Shelf ◽

Depth Profile ◽

Wind Stress ◽

Local Maximum ◽

Far Field ◽

Maximum Frequency ◽

Offshore Structure ◽

Shelf Wave ◽

Shelf Waves ◽

Continental Shelf Waves

Alongshore variations in coastline curvature or offshore depth profile can create localised regions of shelf-wave propagation with modes decaying outside these regions. These modes, termed localised continental shelf waves ($\ell$CSWs) here, exist only at certain discrete frequencies lying below the local maximum frequency, and above the far-field maximum frequency, for propagating shelf waves. The purpose of this paper is to obtain these frequencies and construct, both analytically and numerically, and discuss $\ell$CSWs for shelves with arbitrary alongshore variations in offshore depth profile and coastline curvature. If the shelf curvature changes by a small fraction of its value over the shelf section of interest or an alongshore perturbation in offshore depth profile varies slowly over the same length scale then $\ell$CSWs can be constructed using WKBJ theory. Two subcases are described: (i) if the propagating region is sufficiently long that the offshore structure of the $\ell$CSW varies appreciably alongshore then the frequency and alongshore structure are found from a sequence of local problems; (ii) if the propagating region is sufficiently short that the alongshore change in offshore structure of the $\ell$CSW is small then the alongshore modal structure is given in an explicit, uniformly valid form. A separate asymptotic theory is required for curvature perturbations to shelves that are otherwise straight rather than curved. Comparison with highly accurately numerically determined $\ell$CSWs shows that both theories are extremely accurate, with the WKBJ theory having a significantly wider range of applicability. An idealised model for the generation of $\ell$CSWs is also suggested. A localised time-periodic wind stress generates an evanescent continental shelf wave in the far field of a localised mode where the coast is almost straight and the response on the shelf is obtained numerically. If the forcing frequency is close to that of an $\ell$CSW then the wind stress excites energetic motions in the region of maximum curvature, creating a significant localised response possibly far from the forcing region.

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