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.

Method for Analytical Representation of the Maximum Inaccuracies of Indirectly Measurable Variable

Let us have an indirectly measurable variable which is a function of directly measurable variables. In this survey we present the introduced by us method for analytical representation of its maximum absolute and relative inaccuracy as functions, respectively, of the maximum absolute and of the relative inaccuracies of the directly measurable variables. Our new approach consists of assuming for fixed variables the statistical mean values of the absolute values of the coefficients of influence, respectively, of the absolute and relative inaccuracies of the directly measurable variables in order to determine the analytical form of the maximum absolute and relative inaccuracies of an indirectly measurable variable. Moreover, we give a method for determining the numerical values of the maximum absolute and relative inaccuracies. We define a sample plane of the ideal perfectly accurate experiment and using it we give a universal numerical characteristic – a dimensionless scale for determining the quality (accuracy) of the experiment.

A comparison of the critical impeller speed for solids suspension in a bench-scale and a pilot-scale mechanical flotation cell

This paper compares the critical impeller speed results for 6 L Denver and Wemco bench-scale flotation cells with findings from a study by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2007. Evaluation of solids suspension in a pilot-scale mechanical flotation cell: the critical impeller speed. Minerals Engineering 20,233-240; Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] conducted in a 125 L Batequip flotation cell. Understanding solids suspension has become increasingly important due to dramatic increases in flotation cell sizes. The critical impeller speed is commonly used to indicate the effectiveness of solids suspension. The minerals used in this study were apatite, quartz and hematite. The critical impeller speed was found to be strongly dependent on particle size, solids density and air flow rate, with solids concentration having a lesser influence. Liquid viscosity was found to have a negligible effect. The general Zwietering-type critical impeller speed correlation developed by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] was found to be applicable to all three flotation machines. The exponents for particle size, solids concentration and liquid viscosity were equivalent for all three cells. The exponent for solids density was found to be less significant than that obtained by the previous authors, and to be consistent with values reported in the general literature for stirred tanks. Finally, a new dimensionless critical impeller speed correlation is proposed where the particle size is divided by the impeller diameter. This modified equation generally predicts the experimental measurements well, with most predictions within 10% of the experimental. (C) 2009 Elsevier Ltd. All rights reserved.

Air Bubble Entrainment in Hydraulic Jumps: Physical Modelling and Scale Effects

A hydraulic jump is characterised by strong energy dissipation and air entrainment. In the present study, new air-water flow measurements were performed in hydraulic jumps with partially-developed flow conditions in relatively large-size facilities with phase-detection probes. The experiments were conducted with identical Froude numbers, but a range of Reynolds numbers and relative channel widths. The results showed drastic scale effects at small Reynolds numbers in terms of void fraction and bubble count rate distributions. The void fraction distributions implied comparatively greater detrainment at low Reynolds numbers leading to a lesser overall aeration of the jump roller, while dimensionless bubble count rates were drastically lower especially in the mixing layer. The experimental results suggested also that the relative channel width had little effect on the air-water flow properties for identical inflow Froude and Reynolds numbers.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.

Approach to designing rotating drum bioreactors for solid-state fermentation on the basis of dimensionless design factors

The development of large-scale solid-stale fermentation (SSF) processes is hampered by the lack of simple tools for the design of SSF bioreactors. The use of semifundamental mathematical models to design and operate SSF bioreactors can be complex. In this work, dimensionless design factors are used to predict the effects of scale and of operational variables on the performance of rotating drum bioreactors. The dimensionless design factor (DDF) is a ratio of the rate of heat generation to the rate of heat removal at the time of peak heat production. It can be used to predict maximum temperatures reached within the substrate bed for given operational variables. Alternatively, given the maximum temperature that can be tolerated during the fermentation, it can be used to explore the combinations of operating variables that prevent that temperature from being exceeded. Comparison of the predictions of the DDF approach with literature data for operation of rotating drums suggests that the DDF is a useful tool. The DDF approach was used to explore the consequences of three scale-up strategies on the required air flow rates and maximum temperatures achieved in the substrate bed as the bioreactor size was increased on the basis of geometric similarity. The first of these strategies was to maintain the superficial flow rate of the process air through the drum constant. The second was to maintain the ratio of volumes of air per volume of bioreactor constant. The third strategy was to adjust the air flow rate with increase in scale in such a manner as to maintain constant the maximum temperature attained in the substrate bed during the fermentation. (C) 2000 John Wiley & Sons, Inc.

The effective Planck mass and the scale of inflation

Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation—a priori, one of the more immediate corollaries of detecting primordial tensor modes—one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza–Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.

A theoretical exploration of catchment-scale sediment delivery

This paper proposes a theoretical explanation of the variations of the sediment delivery ratio (SDR) versus catchment area relationships and the complex patterns in the behavior of sediment transfer processes at catchment scale. Taking into account the effects of erosion source types, deposition, and hydrological controls, we propose a simple conceptual model that consists of two linear stores arranged in series: a hillslope store that addresses transport to the nearest streams and a channel store that addresses sediment routing in the channel network. The model identifies four dimensionless scaling factors, which enable us to analyze a variety of effects on SDR estimation, including (1) interacting processes of erosion sources and deposition, (2) different temporal averaging windows, and (3) catchment runoff response. We show that the interactions between storm duration and hillslope/channel travel times are the major controls of peak-value-based sediment delivery and its spatial variations. The interplay between depositional timescales and the travel/residence times determines the spatial variations of total-volume-based SDR. In practical terms this parsimonious, minimal complexity model could provide a sound physical basis for diagnosing catchment to catchment variability of sediment transport if the proposed scaling factors can be quantified using climatic and catchment properties.

Is the Netherlands sustainable as a global-scale inner-city? Intenscoping spatial sustainability

Is the Netherlands sustainable or not? The answer inherently involves addressing the issues of system boundaries, statistical units and a vision of sustainability. As an analytical answer we offer the Intenscope (IS), a two-dimensional graphical tool based on dimensionless percentages of triple rate ratios which overcomes several limitations of sustainability analyses. First, it is not sensitive to the size of statistical units so an area with twice the amount of resources of another, with double the population (and double the total consumption) would have the same triple ratio of population:biocapacity:consumption. Second, the IS is sensitive to anomalies which may originate either from the use of arbitrary statistical units (e.g. the boundaries of a city) or those which may indicate truly unsustainable practices. To judge spatial sustainability we use ecological footprint data from which we construct a plausible country plot based on the IS. Despite the relative nature of IS-analyses, the employed consumption:biocapacity ratio inherently refers to the absolute limit of sustainability: we cannot continually use more resources on a global scale than nature provides us with. The analysis introduces some associations of human preferences and attributions of settlement types which may help to elaborate sustainability policies based on voluntary action.

Validação da Body Appreciation Scale (BAS), Life Satisfaction Index for the Third Age (LSITA) e do Aging Perception Questionnaire (APQ) para a língua portuguesa no Brasil : um estudo em idosos brasileiros

Universidade Estadual de Campinas . Faculdade de Educação Física

Tradução, adaptação cultural e estrutura fatorial do Body Shape Questionnaire, Body Esteem Scale e Body Appreciation Scale para mulheres brasileiras na meia-idade

Universidade Estadual de Campinas . Faculdade de Educação Física

Tradução, adaptação cultural e validação da escala Moorong Self-Efficacy Scale (MSES) para o português no Brasil = : Translation, cultural adaptation and validation of Moorong Self-Efficacy Scale (MSES) into Brazilian Portuguese

Universidade Estadual de Campinas . Faculdade de Educação Física

Adaptação e validação da escla ASKAS - Aging Sexual Knowledge and Attitudes Scale em idosos brasileiros

Universidade Estadual de Campinas . Faculdade de Educação Física

Cross-cultural adaptation, validation and reliability of the Body Area Scale for Brazilian adolescents

The aim of this study was to translate, validate and verify the reliability of the Body Area Scale (BAS). Participants were 386 teenagers, enrolled in a private school. Translation into Portuguese was conducted. The instrument was evaluated for internal consistency and construct validation analysis. Reproducibility was evaluated using the Wilcoxon test and the coefficient of interclass correlation. The BAS demonstrated good values for internal consistency (0.90 and 0.88) and was able to discriminate boys and girls according to nutritional state (p = 0.020 and p = 0.026, respectively). BAS scores correlated with adolescents' BMI (r = 0.14, p = 0.055; r = 0.23, p = 0.001) and WC (r =0.13, p = 0.083; r = 0.22, 0.002). Reliability was confirmed by the coefficient of inter-class correlation (0.35, p < 0.001; 0.60, p < 0.001) for boys and girls, respectively. The instrument performed well in terms of understanding and time of completion. BAS was successfully translated into Portuguese and presented good validity when applied to adolescents.

Psychometric evaluation of the Disordered Eating Attitude Scale (DEAS)

Eating attitudes are defined as beliefs, thoughts, feelings, behaviors and relationship with food. They could influence people’s food choices and their health status. Objective: This study aimed to adapt from Portuguese to English the Disordered Eating Attitude Scale (DEAS) and evaluate its validity and reliability. The original scale in Portuguese was translated and adapted into English and was applied to female university students of University of Minnesota—USA (n = 224). Internal consistency was determined (Cronbach’s Alpha). Convergent validity was assessed by correlations between Eating Attitude Test-26 (EAT-26) and Restrain Scale (RS). Reliability was evaluated applying twice the scale to a sub-sample (n = 30). The scale was back translated into Portuguese and compared with the original version and discrepancies were not found. The internal consistency was .76. The DEAS total score was significantly associated with EAT-26 (r = 0.65) and RS (r = 0.69) scores. The correlation between test–retest was r = 0.9. The English version of DEAS showed appropriate internal consistency, convergent validity and test–retest reliability and will be useful to assess eating attitudes in different population groups in English spoken countries