Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime

We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia–gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia–gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds.

Ionic calcium and pH as predictors of stability of milk to UHT processing

This paper describes the use of pH and calcium ion electrodes for investigating factors affecting the heat stability of UHT milk with added calcium chloride. Calcium chloride was added to raw milk to manipulate ionic calcium and pH to within the range that may be typically encountered in raw milk of different compositions and microbial quality. Addition of only 5 mM calcium chloride was sufficient to induce considerable changes in pH, ionic calcium and ethanol stability and alter its stability to UHT treatment. There was a strong relationship between pH decrease and increase in ionic calcium when pH was reduced, whether by addition of calcium chloride or by acidification. Calcium chloride addition was found to increase sediment formation in UHT treated milk. However, sediment could be reduced by addition of stabilizers. Those most effective were ones which decreased ionic calcium and increased pH, such as trisodium citrate and disodium hydrogen phosphate. Sediment formation following UHT treatment was only slight for milk samples whose ethanol stability was greater than 80%.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.