Ageostrophic effects in rotating stratified flow

We consider the low Rossby number (R) flow of a stratified fluid in a long rotating channel, for which the bottom elevation varies in the downstream direction. The quasi-geostrophic response is shown to be singular at the side walls of the channel, and thus an ageostrophic analysis is necessary even for vanishingly small R. Part of the ageostrophic steady-state response is a modified quasi-geostrophic perturbation trapped near the bottom. A second component which is present even as R approaches zero is an internal Kelvin wave whose vertical wavelength adjusts so that the wave remains stationary with respect to the channel bottom and which propagates energy and momentum to infinite heights in an unbounded channel. The case of a bounded layer of fluid is also considered, and the resonance conditions are given. We also calculate the flow field when the bottom elevation varies in the cross-stream direction. We conclude that stagnation or flow reversal can be caused either by the modified quasi-geostrophic component or by the Kelvin wave and estimate the critical condition by an extrapolation of the perturbation velocity computed from linear theory.

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CURRENT INDUCED BY BREAKING OF INTERNAL KELVIN WAVE ON A UNIFORM SLOPE

PROCEEDINGS OF HYDRAULIC ENGINEERING ◽

10.2208/prohe.51.1385 ◽

2007 ◽

Vol 51 ◽

pp. 1385-1390

Author(s):

Keisuke NAKAYAMA ◽

Takumi MIYAZAWA ◽

Yosuke YAMASHIKI ◽

Kensuke MIYAZAWA ◽

Toshiyuki KANESASHI

Keyword(s):

Kelvin Wave ◽

Internal Kelvin Wave

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Trapped internal gravity waves in a geostrophic boundary current

Journal of Fluid Mechanics ◽

10.1017/s0022112093000448 ◽

1993 ◽

Vol 247 ◽

pp. 205-229

Author(s):

Hong Ma

Keyword(s):

Gravity Waves ◽

Internal Gravity Wave ◽

Internal Gravity Waves ◽

Combined Effects ◽

Kelvin Wave ◽

Boundary Current ◽

Trapping Mechanism ◽

Rossby Radius Of Deformation ◽

Wave Guides ◽

Internal Kelvin Wave

The effect of a geostrophic boundary current on internal gravity waves is studied with a reduced-gravity model. We found that the boundary current not only modifies the coastal Kelvin wave, but also forms wave guides for short internal gravity waves. The combined effects of current shear, the boundary, and the slope of the interface create the trapping mechanism. These trapped internal gravity waves appear as groups of discrete zonal modes. They have wavelengths comparable to or shorter than the internal Rossby radius of deformation. Their phase speeds are close to that of the internal Kelvin wave. However, they can propagate both in, or opposite to, the direction of the Kelvin wave. The results of the present work suggest the possibility of finding an energetic internal gravity wave phenomenon with near-inertial frequency in a broad geostrophic boundary current.

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Meteor radar observations of atmospheric waves in the equatorial mesosphere/lower thermosphere over Ascension Island

Annales Geophysicae ◽

10.5194/angeo-22-387-2004 ◽

2004 ◽

Vol 22 (2) ◽

pp. 387-404 ◽

Cited By ~ 43

Author(s):

D. Pancheva ◽

N. J. Mitchell ◽

P. T. Younger

Keyword(s):

Zonal Wind ◽

Middle Atmosphere ◽

Lower Thermosphere ◽

Meridional Wind ◽

Kelvin Wave ◽

Vertical Wavelength ◽

Period Range ◽

Meridional Component ◽

Ascension Island ◽

Waves And Tides

Abstract. Some preliminary results about the planetary wave characteristics observed during the first seven months (October 2001-April 2002) of observations over Ascension Island (7.9°S, 14.4°W) are reported in this study. The zonal wind is dominated by the 3–7-day waves, while the meridional component – by the quasi-2-day wave. Two wave events in the zonal wind are studied in detail: a 3–4-day wave observed in the end of October/November and the 3–6-day wave in January/February. The moderate 3- and 3.2-day waves are interpreted as an ultra-fast Kelvin wave, while for the strong 4-day wave we are not able to make a firm decision. The 6-day wave is interpreted as a Doppler-shifted 5-day normal mode, due to its very large vertical wavelength (79km). The quasi-2-day wave seems to be present almost continuously in the meridional wind, but the strongest bursts are observed mainly in December and January. The observed period range is large, from 34 to 68h, with some clustering around 43–44 and 50h. The estimated vertical wavelengths indicate shorter lengths during the equinoxes, in the range of 25-30km, and longer ones, ∼40–50km, in January/February, when the 48-h wave is strongest. Key words. Meteorology and atmospheric dynamics middle atmosphere dynamics, waves and tides)

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Internal Kelvin wave frontogenesis on the equatorial pycnocline

Geophysical & Astrophysical Fluid Dynamics ◽

10.1080/03091929.2011.577072 ◽

2011 ◽

Vol 105 (4-5) ◽

pp. 438-452 ◽

Cited By ~ 1

Author(s):

Dmitry V. Stepanov ◽

Vadim Novotryasov

Keyword(s):

Kelvin Wave ◽

Internal Kelvin Wave

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Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel

Nonlinear Processes in Geophysics ◽

10.5194/npg-16-587-2009 ◽

2009 ◽

Vol 16 (5) ◽

pp. 587-598 ◽

Cited By ~ 4

Author(s):

J. C. Sánchez-Garrido ◽

V. Vlasenko

Keyword(s):

Solitary Waves ◽

Nonlinear Effects ◽

Kelvin Waves ◽

Internal Solitary Waves ◽

Kelvin Wave ◽

Weakly Nonlinear ◽

Strongly Nonlinear ◽

Petviashvili Equation ◽

Rotating Channel

Abstract. The evolution of internal solitary waves (ISWs) propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel) with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.

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Degeneration of internal Kelvin waves in a continuous two-layer stratification

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.311 ◽

2015 ◽

Vol 777 ◽

pp. 68-96 ◽

Cited By ~ 12

Author(s):

Hugo N. Ulloa ◽

Kraig B. Winters ◽

Alberto de la Fuente ◽

Yarko Niño

Keyword(s):

Molecular Diffusion ◽

Hydrodynamic Instabilities ◽

Kelvin Wave ◽

Linear Character ◽

Turbulent Transition ◽

Convective Instabilities ◽

Initial Wave ◽

Intensity Parameters ◽

Rossby Radius Of Deformation ◽

Internal Kelvin Wave

We explore the evolution of the gravest internal Kelvin wave in a two-layer rotating cylindrical basin, using direct numerical simulations (DNS) with a hyper-viscosity/diffusion approach to illustrate different dynamic and energetic regimes. The initial condition is derived from Csanady’s (J. Geophys. Res., vol. 72, 1967, pp. 4151–4162) conceptual model, which is adapted by allowing molecular diffusion to smooth the discontinuous idealized solution over a transition scale, ${\it\delta}_{i}$, taken to be small compared to both layer thicknesses $h_{\ell },\ell =1,2$. The different regimes are obtained by varying the initial wave amplitude, ${\it\eta}_{0}$, for the same stratification and rotation. Increasing ${\it\eta}_{0}$ increases both the tendency for wave steepening and the shear in the vicinity of the density interface. We present results across several regimes: from the damped, linear–laminar regime (DLR), for which ${\it\eta}_{0}\sim {\it\delta}_{i}$ and the Kelvin wave retains its linear character, to the nonlinear–turbulent transition regime (TR), for which the amplitude ${\it\eta}_{0}$ approaches the thickness of the (thinner) upper layer $h_{1}$, and nonlinearity and dispersion become significant, leading to hydrodynamic instabilities at the interface. In the TR, localized turbulent patches are produced by Kelvin wave breaking, i.e. shear and convective instabilities that occur at the front and tail of energetic waves within an internal Rossby radius of deformation from the boundary. The mixing and dissipation associated with the patches are characterized in terms of dimensionless turbulence intensity parameters that quantify the locally elevated dissipation rates of kinetic energy and buoyancy variance.

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