The stability of an axially symmetric warm-core model eddy on a stratified ocean

The linear stability of an axially symmetric model of a warm-core eddy over a stratified ocean of infinite depth is investigated using asymptotic techniques for large wavenumber and small Burger number. The development is similar to previous work on the stability of a geostrophic front (Kroll, 1992) and the results found there can be modified and applied to most oceanic eddies. The most important result is that instability occurs in a region confined at the edge of the eddy with maximum width of a fraction of the radius given approximately by the Rossby number for realistic eddies. We expect the instability to produce turbulence and contribute to the breakdown of the interface between the eddy and the surrounding ocean in this region

On the chaotic evolution of baroclinic instability of wave-wave interactions with topography

De Szoeke (1986) developed an asymptotic solution for the nonlinear evolution of a type of baroclinic instability of a two-layer quasi-geostrophic model over topography. He found that under certain conditions pairs of hybrid modes interacting with topography could become unstable in the linearized model. He also found that the addition of the nonlinearity stabilized the flow which he analyzed using an expansion in small ε, a measure of the topographic height. This work is extended and modified by first considering a slightly varying mean flow (time dependent parametric forcing) which produces chaotic behavior, and then considering friction which allows chaos on a strange attractor. This chaos is examined in various ways including using Melnikov\u27s method. The original unforced system without friction can be called critically nonchaotic in that only a very small amount of forcing produces significant chaotic behavior. We then investigate whether the original system can be chaotic without any variation in the mean flow. An additional term is included in the asymptotic system to form a six variable system which can become chaotic. We also look at a more general, nonasymptotic, initial value problem consisting of sixteen variables, assuming small amplitudes, which also can become chaotic. Finally, we consider an asymptotic expansion in small α, the aspect ratio of the top to the bottom layer, assuming ε = O (1), which is often more realistic in the ocean. It is found that at the conditions of greatest initial growth of the amplitudes the system can be chaotic with the largest amplitude in the top layer

Fire, Ice, Water, and Dirt: A Simple Climate Model

A simple paleoclimate model was developed as a modeling exercise. The model is a lumped parameter system consisting of an ocean (water), land (dirt), glacier, and sea ice (ice) and driven by the sun (fire). In comparison with other such models, its uniqueness lies in its relative simplicity yet yielding good results. For nominal values of parameters, the system is very sensitive to small changes in the parameters, yielding equilibrium, steady oscillations, and catastrophes such as freezing or boiling oceans. However, stable solutions can be found, especially naturally oscillating solutions. For nominally realistic conditions, natural periods of order 100kyrs are obtained, and chaos ensues if the Milankovitch orbital forcing is applied. An analysis of a truncated system shows that the naturally oscillating solution is a limit cycle with the characteristics of a relaxation oscillation in the two major dependent variables, the ocean temperature and the glacier ice extent. The key to getting oscillations is having the effective emissivity decreasing with temperature and, at the same time, the effective ocean albedo decreases with increasing glacier extent. Results of the original model compare favorably to the proxy data for ice mass variation, but not for temperature variation. However, modifications to the effective emissivity and albedo can be made to yield much more realistic results. The primary conclusion is that the opinion of Saltzman [Clim. Dyn. 5, 67-78 (1990)] is plausible that the external Milankovitch orbital forcing is not sufficient to explain the dominant 100kyr period in the data. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4991383

An unstable uniform slab model of the mixed layer as a source of downward propagating near-inertial motion Part 2: Unsteady mean flow

The model of the uniform slab model of the mixed layer which was previously analyzed for stability (Kroll, 1982) is modified to include inertial oscillations in the mean flow. The results reflect the nature of the parallel flow instability produced by the steady component of the mean flow combined with the nature of a parametric instability produced by the oscillating component of the mean flow. This model is much more likely to produce unstable perturbations with a near-inertial frequency than the steady mean model which reinforces the contention that the instability can be a source of vertically propagating inertial oscillations. Also certain frequencies that are integral multiples of the inertial frequency above a near-inertial frequency can be significant in the perturbation. The energy flux associated with these frequencies predominates as the inertial oscillations in the mean flow become significant. This could produce a significant energy flux from the mean flow

An unstable uniform slab model of the mixed layer as a source of downward propagating near-inertial motion. Part 1: Steady mean flow

The linear stability of a one layer turbulent slab model of the mixed layer over a continuously stratified, inviscid, infinite depth ocean is investigated for large horizontal scale (≥ 0 (1 km)) perturbations…

The effect of mean flow during an upwelling event on the rays of internal waves

Hayes and Halpern (1976) have calculated the rays associated with internal waves in the semidiurnal frequency range. This they do to show how the change of the trajectories of these rays, due to density changes occurring during an upwelling event, can explain the decrease of semidiumal activity observed at their mooring site. Here we consider the additional effect of the mean flow generated by an upwelling event...

The stability of a canonical front

The stability of a geostrophic frontal current of constant slope over a stratified ocean is investigated using asymptotic techniques for large horizontal wavenumber and a small Burger number. The front is called canonical because it should approximate the edges of eddies or boundary currents. Results show that the front is unstable for an along the front wavenumber greater than f/V0 where V0 is the current velocity. But the instability is confined to a region near the vertex of the front of horizontal extent 0(V0/f). The flow becomes more unstable for increasing wavenumber and it is speculated that this region near the vertex will be strongly mixed, rounding off the sharp vertex of the steady state flow. There will be strong internal wave propagation from the interface of this region into the ocean when the frequency is greater than f

The propagation of wind-generated inertial oscillations from the surface into the deep ocean

The object of this study is to explain the occurrence of relatively large amplitude inertial motion observed at great depths in the ocean. An arbitrarily stratified, β-plane model is considered consisting of a viscous boundary layer at the surface and an inviscid interior. The forcing due to a wind stress produces Ekman suction in the boundary layer which in turn drives the interior. Ray theory is then used to describe the propagation of disturbances in the boundary layer down into the interior...

Enhanced microbial activity in carbon-rich pillow lavas, Ordovician, Great Britain and Ireland

Date of acceptance: 09/07/2015 ACKNOWLEDGEMENTS A. Sandison and C. Taylor provided skilled technical support. Boyce is funded by Natural Environment Research Council (NERC) support of the Isotope Community Support Facility at the Scottish Universities Environmental Research Centre. NERC supported the project through facility grant IP-1235- 0511. The Raman spectroscopy facility at the University of Aberdeen is funded by the Biotechnology and Biological Sciences Research Council. We are grateful to M. Feely, G. Purvis, and an anonymous reviewer for helpful criticism.Peer reviewedPostprin

Representation of Secondary Organic Aerosol Laboratory Chamber Data for the Interpretation of Mechanisms of Particle Growth

Absorptive models of gas-particle partitioning have been shown to be successful in describing the formation and growth of secondary organic aerosol (SOA). Here the expression for particle growth derived by Odum et al. (Odum, J. R.; Hoffmann, T.; Bowman, F.; Collins, D.; Flagan, R. C.; Seinfeld, J. H. Gas/particle partitioning and secondary organic aerosol yields. Environ. Sci. Technol. 1996, 30, 2580−2585) is extended to facilitate interpretation of SOA growth data measured in the laboratory in terms of the underlying chemistry, even when details of the reactions are not well-constrained. A simple (one-component) expression for aerosol growth (ΔM) as a function of the amount of hydrocarbon reacted (ΔHC) is derived, and the effects of changes to three key parameters, stoichiometric yield of condensable species, gas-particle partitioning coefficient, and concentration of preexisting aerosol, are discussed. Two sets of laboratory chamber data on SOA growth are examined in this context:  the ozonolysis of α-pinene and the OH-initiated photooxidation of aromatic compounds. Even though these two systems have a number of significant differences, both are described well within this framework. From the shapes of the ΔM versus ΔHC curves in each case, the importance of poorly constrained chemistry such as heterogeneous reactions and gas-phase reactions of oxidation products is examined