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.

Is optical imaging spectroscopy a viable measurement technique for the investigation of the negative BOLD phenomenon? A concurrent optical imaging spectroscopy and fMRI study at high field (7T)

Traditionally functional magnetic resonance imaging (fMRI) has been used to map activity in the human brain by measuring increases in the Blood Oxygenation Level Dependent (BOLD) signal. Often accompanying positive BOLD fMRI signal changes are sustained negative signal changes. Previous studies investigating the neurovascular coupling mechanisms of the negative BOLD phenomenon have used concurrent 2D-optical imaging spectroscopy (2D-OIS) and electrophysiology (Boorman et al., 2010). These experiments suggested that the negative BOLD signal in response to whisker stimulation was a result of an increase in deoxy-haemoglobin and reduced multi-unit activity in the deep cortical layers. However, Boorman et al. (2010) did not measure the BOLD and haemodynamic response concurrently and so could not quantitatively compare either the spatial maps or the 2D-OIS and fMRI time series directly. Furthermore their study utilised a homogeneous tissue model in which is predominantly sensitive to haemodynamic changes in more superficial layers. Here we test whether the 2D-OIS technique is appropriate for studies of negative BOLD. We used concurrent fMRI with 2D-OIS techniques for the investigation of the haemodynamics underlying the negative BOLD at 7 Tesla. We investigated whether optical methods could be used to accurately map and measure the negative BOLD phenomenon by using 2D-OIS haemodynamic data to derive predictions from a biophysical model of BOLD signal changes. We showed that despite the deep cortical origin of the negative BOLD response, if an appropriate heterogeneous tissue model is used in the spectroscopic analysis then 2D-OIS can be used to investigate the negative BOLD phenomenon.

The history of entrepreneurship: Medieval origins of a modern phenomenon

The origins of enterprise are often associated with the Industrial Revolution, but this article presents evidence of entrepreneurial activities from a much earlier date – the medieval period. Between 1250 and 1500 the church, merchants and members of the royal court all engaged in activities that demonstrated the entrepreneurial characteristics of innovation, risk-taking and judgement. The activities of the prior of Tynemouth and the career of the wool merchant William de la Pole illustrate these developments. By focusing on individuals rather than firms, it is possible to push back the study of entrepreneurship beyond the Industrial Revolution and early-modern trade to a period that witnessed the origins of the modern state.

Is it still King Lear? English teachers and the e-reader phenomenon

E-reading devices such as the Kindle have rapidly secured a significant place in a number of societies as at least one major platform for reading.To some extent they are part of the overarching move towards a fully digitised world, but they have a distinctiveness in being deliberately‘book-like’. Teachers generally have some suspicion towards ‘New Media’, especially when it challenges their established practice. This chapter reports on a survey of English teachers in England to gauge their reactions to e-readers, both personally and professionally, and describes their speculations about the place of e-readers in schools in the future. There is a mixed reaction with some teachers concerned about the demise of the book and the potential negative impact on reading. However, the majority welcome e-readers as a dynamic element within the reading environment with particular potential to enthuse reluctant readers and those with special or linguistic needs. They also, some grudgingly, view the fact that reading using this form of technology appeals to the ‘egeneration’ and may succeed in making reading ‘cool’. This form of technology is, ironically [given that it appears to threaten traditional books], likely to be rapidly adopted in classrooms.

The ratio bias phenomenon: fact or artifact?

The ratio bias—according to which individuals prefer to bet on probabilities expressed as a ratio of large numbers to normatively equivalent or superior probabilities expressed as a ratio of small numbers—has recently gained momentum, with researchers especially in health economics emphasizing the policy importance of the phenomenon. Although the bias has been replicated several times, some doubts remain about its economic significance. Our two experiments show that the bias disappears once order effects are excluded, and once salient and dominant incentives are provided. This holds true for both choice and valuation tasks. Also, adding context to the decision problem does not alter this finding. No ratio bias could be found in between-subject tests either, which leads us to the conclusion that the policy relevance of the phenomenon is doubtful at best.

The urban cool island phenomenon in a high-rise high-density city and its mechanisms

The urban heat island (UHI) phenomenon has been studied extensively, but there are relatively fewer reports on the so-called urban cool island (UCI) phenomenon. We reveal here that the UCI phenomenon exists in Hong Kong during the day, and is associated with the UHI at night under all wind and cloud conditions. The possible mechanisms for the UCI phenomenon in such a high-rise compact city have been discovered using a lumped urban air temperature model. A new concept of urban cool island degree hours (UCIdh) to measure the UCI intensity and duration is proposed. Our analyses reveal that when anthropogenic heat is small or absent, a high-rise and high-density city experiences a significant daytime UCI effect. This is explained by an intensified heat storage capacity and the reduced solar radiation gain of urban surfaces. However, if anthropogenic heat in the urban area increases further, the UCI phenomenon still exists, yet UCIdh decrease dramatically in a high-rise compact city. In a low-rise, low-density city, the UCI phenomenon also occurs when there is no anthropogenic heat, but easily disappears when there is little anthropogenic heat, and the UHI phenomenon dominates. This probably explains why the UHI phenomenon is often observed, but the UCI phenomenon is rarely observed. The co-existence of urban heat/cool island phenomena implies reduction of the daily temperature range (DTR) in such cities, and its dependence on urban morphology also implies that urban morphology can be used to control the urban thermal environment.

The only way is up: retail format saturation and the demise of the American five and dime store, 1914-1941

We examine a classic ‘wheel of retailing’ episode – the abandonment of the five and dime pricing formula by American variety chains. These switched from a conventional product lifecycle, focusing on cost reduction through standardisation, to a reverse path up the ‘service cost - unit value’ continuum. We show that, rather than reflecting deteriorating managerial acumen, this was a response to the continued imperative for growth following retail format saturation. Firm-specific (rather than format-specific) competitive advantages were too weak for any chain to be confident it could win a within-format price war, making inter-format competition through raising price points more attractive.