Kelvin waves

The dynamics behind the Kelvin wave front changes completely. The divergence of the Ekman offshore transport is balanced by the divergence of the coastal jet in the surface layer and the divergence of the Ekman compensation current in the sub-thermocline layer is balanced by the longshore divergence of a coastal undercurrent flowing in opposite direction to the upper layer coastal jet. 

The arbitrary longshore shape of the wave described by G x — ci) remains unchanged while propagating along the coast and can be of a localized or a sinusoidal pattern. The Kelvin wave is trapped in a coastal wave guide along the coast and is not felt offshore of this guide with the width determined by the Rossby radius. Barotropic Kelvin waves have a wide Rossby radius of the order of = 0(100 km) and baroclinic waves a Rossby radius of the order of R = 0(5 km) in the Baltic Sea. 

The impact on a Kelvin wave on upwelling on irregular curved coastlines is described already in Section 2.3.2. Additionally, the Kelvin wave can export up- or downweUing from a coastal segment where it is forced directly by the wind into a coastal segment positioned into the direction of the Kelvin wave propagation where no upwelling is directly forced because the wind blows onshore or offshore. 

Moreover, the Kelvin wave can control the water exchange between two basins connected by a channel. The basic physics of this process can be reduced to the Rossby adjustment process in a channel of uniform depth and uniform width. This problem was considered theoretically by Gill (1976) as an initial problem with a steplike sea level distribution in the channel. The results are similar for abarotropic and a baroclinic two-layer flow however, the sea level elevation must be replaced by the elevation of the interface and the barotropic long wave phase velocity by the baroclinic phase velocity, which is much smaller than the barotropic velocity. This implies that the baroclinic Rossby radius is more than one order of magnitude smaller than the barotropic radius. 

Kelvin waves require a flat-bottomed ocean, so the coastal boundary needs to be a vertical cliff. In a real ocean, there is a topographic transition from the coastline to the central plain areas of the basin. We denote this transition region as shelf. If the horizontal scale of the shelf is small compared with the internal Rossby radius, the Kelvin wave is the most important... 

It is illuminating to study the time evolution of a river plume as an initial value problem. It can be shown that the current pattern is governed by a geostrophically adjusted eddy confined to the buoyancy patch (near field) and a coastally trapped flow that develops in the wake of a Kelvin wave (far field). Behind the front of the first Kelvin wave mode, undercurrents are set up. Although the velocities of the flow forced by the momenrnm of the river mnoff are small enough to justify a linear treatment, there are important nonlinear effects owing to the advection of density, which limits the validity of the linear analytical models. In particular, the structure of the near field in front of the river mouth is dominated by the response to the buoyancy flux associated with the river discharge. 

The numerical models can give accurate representations of the response scenario, that is, the formation of the bulge off the river mouth, alongshore propagating Kelvin waves, the... 

Figure 3.14 Geopotential and wind structure of an equatorial Kelvin wave (upper panel) and mixed Rossby-gravity wave (lower panel).

Maxworthy, T. (1983). Experiments on solitary internal Kelvin waves. JFM129 365-383. Monismith, S.G., Maxworthy, T. (1989). Selective withdrawal and spin-up of a rotating. 

Kelvin wave An eastward-propagating gravity wave modified by the Earth s rotation. Its structure is symmetric about the equator and depends on the change of sign of the Coriolis force across the equator. 

Wave motions on a variety of scales are common in the tropics and, as noted earlier, some of these are thought to play a central role in bringing about the oscillations of the zonal-mean wind system. Best documented among these are the large-scale Kelvin and Rossby-gravity waves. Figure 12 shows the horizontal structure of an equatorial Kelvin wave the dynamics of the wave are discussed in Section IV.B.4. 

FIGURE 12 Schematic representation of the horizontal structure of an equatorial Kelvin wave. The contours denote geopotential anomalies, while the arrows denote zonal wind perturbations. Note that the Kelvin wave has no meridional wind perturbation. [From Andrews etal. (1987). Middle Atmosphere Dynamics, Academic Press, New York.]... 

The salient characteristic of the Kelvin wave is that it has no meridional motion held air motions induced by this type of wave take place exclusively in the longitude-altitude plane. The equations governing the Kelvin wave are thus a subset of (24)-(28) ... 

The characteristic Gaussian structure of the Kelvin wave was illustrated in Fig. 12. In other respects, the Kelvin wave resembles the gravity waves discussed in Section rV.B. 1 in particular, its dispersion relation is... 

Kelvin waves figure prominently in observations of the stratospheric wave field in the tropics. They are known to play a major role in driving the eastward phase of the SAO in the upper stratosphere (see Section IV. A.4). 

FIGURE 4 Dispersion diagram for the equatorial -plane (a) inertia-gravity waves and the Kelvin wave, (b) Rossby waves and the mixed Rossby-gravity wave. (Note different scales along the ordinates). The nondimensional frequency is a and the nondimensional zonal wavenumber is /c. Curves are labeled by the index n corresponding to different meridional structures. See text for additional details. 

Vertically propagating Kelvin and mixed Rossby-gravity modes have been identified in the stratosphere the evidence in the troposphere is less clear. Internal oceanic Kelvin waves are considered by many oceanographers to be the piimaiy mechanism for the eastward transport of heat along the equator associated with the significant in-terarmual phenomenon known as the El Nino/Southem oscillation (ENSO), which affects weather and chmate globally. 

Actually, Kelvin waves were originally named for midlatitude oceanic waves that propagate along a coastline with vanishing velocity component normal to the coast. The classical Kelvin waves are in fact a special case of the inertial-gravity waves with the dispersion relation of Eq. (89). If X is the coordinate along the coast, y is directed toward the water, and the midlatitude /-plane assumption is made, d = 0 is a solution to Eq. (86) if... 

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