Wave propagation and growth on a surface front in a two-layer geostrophic current

Killworth, Peter D.; Paldor, Nathan; Stern, Melvin E.

doi:10.1357/002224084788520701

Cited by 101 publications

(91 citation statements)

References 11 publications

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“…These observations are consistent with baroclinic instability and the propagation of wavelike meanders along the front (Hoskins and Bretherton, 1972;Munk et al, 2000). Killworth et al (1984), considered a two layer model of a front similar to that found in our observations. Their model was set in a semi-infinite domain with an upper layer that vanished at some average position in the y axis direction forming a surface front (Figure 9).…”

Section: ) Instability Of the Almeria-oran Frontsupporting

confidence: 90%

“…These maps suggest that the regions of high cyclonic vorticity propagate along the front. The direction of subduction of MSW discussed in section 2 and the frontal model of Killworth et al (1984), discussed at the beginning of this section, suggest that we can assume the direction of propagation of these vorticity anomalies is the same as that of the mean flow. Therefore, by inspection of Figure 12, we estimate that the wavelength and phase speed of these features are ~ 90 km and order 10 cms -1 respectively.…”

Section: ) Instability Of the Almeria-oran Frontmentioning

confidence: 91%

“…A detailed analysis of the model was presented both in the original paper and by Allen et al (1994), therefore we chose not to repeat this discussion here. Following Killworth et al (1984), the wavelength of the fastest growing mode of instability is given as…”

Section: ) Instability Of the Almeria-oran Frontmentioning

confidence: 99%

“…Perhaps more significantly, Killworth et al (1984) derived an equation for the growth of the zonally averaged total perturbation energy. This separated the relative importance of horizontal and vertical shear processes in the growth of instability.…”

Section: ) Instability Of the Almeria-oran Frontmentioning

confidence: 99%

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Mesoscale subduction at the Almeria–Oran front

Allen

Smeed

Tintoré

et al. 2001

Journal of Marine Systems

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This paper presents a detailed diagnostic analysis of hydrographic and current meter data from three, rapidly repeated, fine-scale surveys of the Almeria-Oran front.Instability of the frontal boundary, between surface waters of Atlantic and Mediterranean origin, is shown to provide a mechanism for significant heat transfer from the surface layers to the deep ocean in winter. The data were collected during the second observational phase of the EU funded OMEGA project on RRS Discovery cruise 224 during December 1996. High resolution hydrographic measurements using the towed undulating CTD vehicle, SeaSoar,. traced the subduction of Mediterranean Surface Water across the Almeria-Oran front. This subduction is shown to result from a significant baroclinic component to the instability of the frontal jet. The Qvector formulation of the omega equation is combined with a scale analysis to quantitatively diagnose vertical transport resulting from mesoscale ageostrophic circulation. The analyses are presented and discussed in the presence of satellite and airborne remotely sensed data; which provide the basis for a thorough and novel approach to the determination of observational error.

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Section: ) Instability Of the Almeria-oran Frontsupporting

confidence: 90%

Section: ) Instability Of the Almeria-oran Frontmentioning

confidence: 91%

Section: ) Instability Of the Almeria-oran Frontmentioning

confidence: 99%

Section: ) Instability Of the Almeria-oran Frontmentioning

confidence: 99%

See 2 more Smart Citations

Mesoscale subduction at the Almeria–Oran front

Allen

Smeed

Tintoré

et al. 2001

Journal of Marine Systems

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“…Surface tracers reveal that the surface flow speed above the annulus is approximately equal to the phase speed of the instability, thus showing that the surface flow dynamics cannot be neglected when considering the evolution of dense eddies. (By analogy, if fluid was injected from the surface, this would induce a flow in the underlying ambient and one would expect the resulting instability to be qualitatively different from that described by Killworth, Paldor & Stern (1984) and Paldor & Killworth (1987), who likewise assumed a stationary ambient.) If the density of the bottom current is relatively small, the observed instability of the current is driven entirely by barotropic instability of the surface jet.…”

Section: Discussionmentioning

confidence: 97%

Rotating dense currents on a slope. Part 1. Stability

et al. 2004

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Using a novel experimental set-up, we examine the stability of an axisymmetric dense current of fluid on a sloping bottom in a rotating frame of reference. In a cylindrical tank on a rotating table, saline fluid is injected through an annular mesh encircling a cone of 1/15 slope. The resulting ring of fluid becomes unstable to periodic sinusoidal waves, whose characteristics are examined as a function of the ambient fluid depth, the rotation rate, and the salinity and depth of the dense current, the latter being related to the injection time. For experiments with relatively low-salinity currents, we find the phase speed of the instability is proportional to the rotation rate, Ω, rather than being proportional to the Nof speed, which varies as 1/Ω. Likewise, the number of waves observed is found to be inconsistent with existing theories for baroclinic instability of a dense current on a sloping bottom with a stationary ambient.Surface tracers reveal that significant currents are induced in the ambient by the injection of the saline fluid and we propose that it is the coupling between the surface and bottom flow that ultimately controls the observed dynamics. In particular, we propose that barotropic instability of the surface flow controls the behaviour of the low-salinity current and, using potential vorticity conservation, we predict the phase speed of the instability should indeed be proportional to Ω. The experimental results are also compared with related work in which eddies and Ekman layers evolve from dense fluid injected from a localized source.

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Linear instability of constant PV cold‐core eddies in a two‐layer ocean

Cohen

Dvorkin

Paldor

2015

Quart J Royal Meteoro Soc

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The linear instability of a constant potential vorticity cold-core eddy is studied in a two-layer shallow water model. The basic state consists of the nonlinear gradient balance with uniform potential vorticity, and in a cold-core eddy these two relations have no analytic solution. Numerical solutions of the basic state structure provide a functional relation between the maximum tangential velocity and the ratio of the eddy's maximal depth and its radius. The maximal growth rates of small amplitude wavelike disturbances are found numerically by employing the shooting to fitting point method, applied in a way that guarantees the regularity of the solutions at the singular points: infinity, eddy centre and the radius where the interface outcrops. Our results show that wave-numbers 2, 3 and 4 are unstable with growth rates of the order of 1 day at small ocean depth and that the growth rates decay with the ocean depth. The instabilities result from the interaction between a lower-layer Rossby wave and an upper-layer Frontal wave. An energy equation for the perturbations shows that the decay of the growth rates with the increase in ocean depth results from the decay of both the Reynolds Stress in the upper layer and the baroclinic energy conversion between the two layers. The decay of the Reynolds Stress with ocean depth was not found in studies of ocean currents which explains the fact that eddies become stable in a 1 1 / 2 -layer model while currents can be unstable at large ocean depth. Comparison with long-lived eddies in the ocean suggests that the current model should be made more realistic before it can be applied to observed eddies.

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Wave propagation and growth on a surface front in a two-layer geostrophic current

Cited by 101 publications

References 11 publications

Mesoscale subduction at the Almeria–Oran front

Mesoscale subduction at the Almeria–Oran front

Rotating dense currents on a slope. Part 1. Stability

Linear instability of constant PV cold‐core eddies in a two‐layer ocean

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