Stratified rotating edge waves

Smith, Stefan G. Llewellyn

doi:10.1017/s002211200300702x

Cited by 12 publications

(18 citation statements)

References 22 publications

(23 reference statements)

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“…In §3 the offshore modal structure is of horizontal scale commensurate with the scale of offshore depth variation and the slow variation in the WKBJ analysis is alongshore. This differs from the WKBJ analysis in Shen et al (1968) for non-rotating free-surface waves and for rotating, stratified edge waves in Zhevandrov (1991), Smith (2004) and Adamou et al (2007) where the alongshore profile is fixed and the waves are short compared to the scale of offshore variations. Topography varying slowly in both horizontal directions is considered for non-rotating free-surface waves by Keller (1958), short topographic Rossby waves in Smith (1970), trapped modes in quantum rings by Gridin et al (2004) and Bruno-Alfonso & Latgé (2008), trapped modes in elastic plates by Gridin et al (2005) and trapped modes in slowly-varying acoustic waveguides by Biggs (2012).…”

Section: Introductionmentioning

confidence: 63%

Localised continental shelf waves: geometric effects and resonant forcing

Rodney

Johnson

2015

J. Fluid Mech.

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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 ( CTWs) here, exist only at certain discrete frequencies lying below the maximum frequency for propagating shelf waves. The purpose of this paper is to obtain these frequencies and construct, both analytically and numerically, and discuss CTWs 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 a alongshore perturbation in offshore depth profile varies slowly over the same length scale then CTWs can be constructed using WKBJ theory. Two subcases are described: (i) if the propagating region is sufficiently long that the offshore structure of the CTW 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 CTW 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 CTWs shows that both theories are extremely accurate with the WKBJ theory having a significantly wider range of applicability and remaining accurate even when the underlying shelf curvature is small. An idealised model for the generation of CTWs 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 CTW then the wind stress excites energetic motions in the region of maximum curvature, creating a significant localised response far from the forcing region.

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Section: Introductionmentioning

confidence: 63%

Localised continental shelf waves: geometric effects and resonant forcing

Rodney

Johnson

2015

J. Fluid Mech.

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“…The total Lagrangian drift current can be written as the sum of the Stokes drift (Stokes 1847) and a mean Eulerian current (see, e.g., Longuet-Higgins 1953). In the present paper the Eulerian current arises as a balance between the radiation stresses, the Coriolis force, and bottom friction.…”

Section: Introductionmentioning

confidence: 92%

“…Denoting the kinematic viscosity by n, the boundary layer thickness d in a nonrotating ocean becomes d 5 (2n/jvj) 1/2 (Longuet-Higgins 1953). In a turbulent ocean, n is the eddy viscosity and may take different values in the top and bottom boundary layers.…”

Section: Linear Wavesmentioning

confidence: 99%

“…Following Longuet-Higgins (1953), the Stokes drift to second order in wave steepness for this problem is easily obtained from the linear wave solutions (23)-(25).…”

Section: The Mean Flowmentioning

confidence: 99%

“…The edge wave problem has also been carried on to a stratified ocean (Greenspan 1970). A thorough discussion of the linear edge wave problem in a rotating ocean with continuous stratification can be found in Llewellyn Smith (2004). Finally, the nonlinear wave drift in interfacial edge waves in a rotating viscous ocean has been investigated by Weber and Støylen (2011), using a shallow-water approach.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mass Transport in the Stokes Edge Wave for Constant Arbitrary Bottom Slope in a Rotating Ocean

Ghaffari

Weber

2014

Journal of Physical Oceanography

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The Lagrangian mass transport in the Stokes surface edge wave is obtained from the vertically integrated equations of momentum and mass in a viscous rotating ocean, correct to the second order in wave steepness. The analysis is valid for bottom slope angles b in the interval 0 , b # p/2. Vertically averaged drift currents are obtained by dividing the fluxes by the local depth. The Lagrangian mean current is composed of a Stokes drift (inherent in the waves) plus a mean Eulerian drift current. The latter arises as a balance between the radiation stresses, the Coriolis force, and bottom friction. Analytical solutions for the mean Eulerian current are obtained in the form of exponential integrals. The relative importance of the Stokes drift to the Eulerian current in their contribution to the Lagrangian drift velocity is investigated in detail. For the given wavelength, the Eulerian current dominates for medium and large values of b, while for moderate and small b, the Stokes drift yields the main contribution to the Lagrangian drift. Because most natural beaches are characterized by moderate or small slopes, one may only calculate the Stokes drift in order to assess the mean drift of pollution and suspended material in the Stokes edge wave. The main future application of the results for large b appears to be for comparison with laboratory experiments in rotating tanks.

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Trapped diurnal internal tides, propagating semidiurnal internal tides, and mixing estimates in the California Current System from sustained glider observations, 2006–2012

Johnston

Rudnick

2015

Deep Sea Research Part II: Topical Studies in Oceanography

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Stratified rotating edge waves

Cited by 12 publications

References 22 publications

Localised continental shelf waves: geometric effects and resonant forcing

Localised continental shelf waves: geometric effects and resonant forcing

Mass Transport in the Stokes Edge Wave for Constant Arbitrary Bottom Slope in a Rotating Ocean

Trapped diurnal internal tides, propagating semidiurnal internal tides, and mixing estimates in the California Current System from sustained glider observations, 2006–2012

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