Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

Unconscious effects of language-specific terminology on pre-attentive colour perception

It is now established that native language affects one's perception of the world. However, it is unknown whether this effect is merely driven by conscious, language-based evaluation of the environment or whether it reflects fundamental differences in perceptual processing between individuals speaking different languages. Using brain potentials, we demonstrate that the existence in Greek of 2 color terms—ghalazio and ble—distinguishing light and dark blue leads to greater and faster perceptual discrimination of these colors in native speakers of Greek than in native speakers of English. The visual mismatch negativity, an index of automatic and preattentive change detection, was similar for blue and green deviant stimuli during a color oddball detection task in English participants, but it was significantly larger for blue than green deviant stimuli in native speakers of Greek. These findings establish an implicit effect of language-specific terminology on human color perception.

Cognitive representation of colour in bilinguals: the case of Greek blues

A number of recent studies demonstrate that bilinguals with languages that differ in grammatical and lexical categories may shift their cognitive representation of those categories towards that of monolingual speakers of their second language. The current paper extended that investigation to the domain of colour in Greek–English bilinguals with different levels of bilingualism, and English monolinguals. Greek differentiates the blue region of colour space into a darker shade called ble and a lighter shade called ghalazio. Results showed a semantic shift of category prototypes with level of bilingualism and acculturation, while the way bilinguals judged the perceptual similarity between within- and cross-category stimulus pairs depended strongly on the availability of the relevant colour terms in semantic memory, and the amount of time spent in the L2-speaking country. These results suggest that cognition is tightly linked to semantic memory for specific linguistic categories, and to cultural immersion in the L2-speaking country.

Perceptual shift in bilingualism: brain potentials reveal plasticity in pre-attentive colour perception

The validity of the linguistic relativity principle continues to stimulate vigorous debate and research. The debate has recently shifted from the behavioural investigation arena to a more biologically grounded field, in which tangible physiological evidence for language effects on perception can be obtained. Using brain potentials in a colour oddball detection task with Greek and English speakers, a recent study suggests that language effects may exist at early stages of perceptual integration [Thierry, G., Athanasopoulos, P., Wiggett, A., Dering, B., & Kuipers, J. (2009). Unconscious effects of language-specific terminology on pre-attentive colour perception. Proceedings of the National Academy of Sciences, 106, 4567–4570]. In this paper, we test whether in Greek speakers exposure to a new cultural environment (UK) with contrasting colour terminology from their native language affects early perceptual processing as indexed by an electrophysiological correlate of visual detection of colour luminance. We also report semantic mapping of native colour terms and colour similarity judgements. Results reveal convergence of linguistic descriptions, cognitive processing, and early perception of colour in bilinguals. This result demonstrates for the first time substantial plasticity in early, pre-attentive colour perception and has important implications for the mechanisms that are involved in perceptual changes during the processes of language learning and acculturation.

Stylised worlds: Colour Separation Overlay in BBC television plays of the 1970s

This essay aims to understand and interrogate the use of Colour Separation Overlay (CSO) as a mode of experimental production and aesthetic innovation in television drama in the 1970s. It sets out to do this by describing, accounting for and evaluating CSO as a production technique, considering the role of key production personnel, and analysing four specific BBC productions. Deploying methodologies of archival research, practitioner interview, and close textual analysis, the essay also delivers a significant reassessment of the role of the producer and designer in the conceptualisation and realisation of small-screen dramatic fiction.

Visual sensor fusion for active security in robotic industrial environments

This work presents a method of information fusion involving data captured by both a standard CCD camera and a ToF camera to be used in the detection of the proximity between a manipulator robot and a human. Both cameras are assumed to be located above the work area of an industrial robot. The fusion of colour images and time of light information makes it possible to know the 3D localization of objects with respect to a world coordinate system. At the same time this allows to know their colour information. Considering that ToF information given by the range camera contains innacuracies including distance error, border error, and pixel saturation, some corrections over the ToF information are proposed and developed to improve the results. The proposed fusion method uses the calibration parameters of both cameras to reproject 3D ToF points, expressed in a common coordinate system for both cameras and a robot arm, in 2D colour images. In addition to this, using the 3D information, the motion detection in a robot industrial environment is achieved, and the fusion of information is applied to the foreground objects previously detected. This combination of information results in a matrix that links colour and 3D information, giving the possibility of characterising the object by its colour in addition to its 3D localization. Further development of these methods will make it possible to identify objects and their position in the real world, and to use this information to prevent possible collisions between the robot and such objects.

Visual sensor fusion for active security in robotic industrial environments

This work presents a method of information fusion involving data captured by both a standard charge-coupled device (CCD) camera and a time-of-flight (ToF) camera to be used in the detection of the proximity between a manipulator robot and a human. Both cameras are assumed to be located above the work area of an industrial robot. The fusion of colour images and time-of-flight information makes it possible to know the 3D localization of objects with respect to a world coordinate system. At the same time, this allows to know their colour information. Considering that ToF information given by the range camera contains innacuracies including distance error, border error, and pixel saturation, some corrections over the ToF information are proposed and developed to improve the results. The proposed fusion method uses the calibration parameters of both cameras to reproject 3D ToF points, expressed in a common coordinate system for both cameras and a robot arm, in 2D colour images. In addition to this, using the 3D information, the motion detection in a robot industrial environment is achieved, and the fusion of information is applied to the foreground objects previously detected. This combination of information results in a matrix that links colour and 3D information, giving the possibility of characterising the object by its colour in addition to its 3D localisation. Further development of these methods will make it possible to identify objects and their position in the real world and to use this information to prevent possible collisions between the robot and such objects.

Colour relationalism and the real deliverances of introspection

Colour relationalism holds that the colours are constituted by relations to subjects. Anti-relationalists have claimed that this view stands in stark contrast to our phenomenally-informed, pre-theoretic intuitions. Is this claim right? Cohen and Nichols’ recent empirical study suggests not, as about half of their participants seemed to be relationalists about colour. Despite Cohen and Nichols’ study, we think that the anti-relationalist’s claim is correct. We explain why there are good reasons to suspect that Cohen and Nichols’ experimental design skewed their results in favour of relationalism. We then run an improved study and find that most of our participants seem to be anti-relationalists. We find some other interesting things too. Our results suggest that the majority of ordinary people find it no less intuitive that colours are objective than that shapes are objective. We also find some evidence that when those with little philosophical training are asked about the colours of objects, their intuitions about colour and shape cases are similar, but when asked about people’s colour ascriptions, their intuitions about colour and shape cases differ.