On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Quantifying time scales of pedogenic calcrete formation using U-series disequilibria

Time scales of pedogenic calcrete development are quantified by subsampling carbonate from within a mature (stage V) pedogenic calcrete profile from southeast Spain and dating the material by U-series disequilibria. The location of the earliest and latest cements can be estimated by comparing previous studies of calcrete morphological development with micromorphological analysis of the study profile. Carbonate was sampled and dated from three locations within the profile: (1) below the lower surface of clasts within the hardpan (representing the earliest cement present-207 +/- 11 ka), (2) from the centre of cement filled pores within the hardpan (reflecting the final plugging of the calcrete hardpan-155 +/- 9 ka) and (3) from the laminar calcrete overlying the hardpan (representing the latest cement-112 +/- 15 ka). These results show that the hardpan took between 73 and 31 ka to form, whilst the mature stage V profile took between 121 and 69 ka to form. This is the first time that rates of mature calcrete development have been established by direct radiometric dating of the authigenic carbonate. The technique is appropriate for dating mature calcretes in dryland regions worldwide and offers the opportunity of increasing our understanding of the spatial and temporal variability in rates of pedogenic calcrete development. (C) 2004 Elsevier B.V. All rights reserved.

An ichnofabric approach to the depositional interpretation of the intensely burrowed Bateig Limestone, Miocene, SE Spain

The foraminiferal-rich pelagic Bateig Limestone forms several varieties of the important building stones quarried at Bateig Hill in southeastern Spain. Three principal ichnofabrics (Bichordites, mottled-Palaeophycus and mottled-Ophiomorpha) are recognized, which are present in at least two (possibly up to four) repeated successions (cycles). Each succession begins with an erosional event. The Bichordites ichnofabric represents a new type of facies, formed as thin turbidity/grain flow, stratiform units derived from sediment slips off a fault into deep water. Each slipped unit became almost completely bioturbated by infaunal echinoids, colonizing by lateral migration. Because of the thinness of the units, successive colonizations tended to truncate the underlying burrows giving rise to a pseudo-stratification. As the Bichordites ichnofabric accumulated on the fault apron, thus reducing the effective height of the fault scarp, the substrate gradually came under the influence of currents traversing the shelf. This led to a change in hydraulic regime, and to the mottled-Palaeophycus and mottled-Ophiomorpha ichnofabrics in sediment deposited under bed load transport, and associated with laminar and cross-stratified beds and local muddy intervals. Reactivation of the fault triggered erosion and channeling and a return to grain flow sedimentation, and to the Bichordites ichnofabric of the succeeding cycle. The highest unit of the Bateig Limestone is formed entirely of cross-stratified calcarenites with occasional Ophiomorpha (Ophiomorpha-primary lamination ichnofabric) and is similar to many shallow marine facies but they still bear a significant content of pelagic foraminifera. The sedimentary setting bears resemblance with that described for the Pleistocene Monte Torre Paleostrait and the modem Strait of Messina (Italy), where the narrow morphology of the depositional area enhanced tidal currents and allowed for high-energy sandy deposition in relatively deep areas. More data on the Miocene paleogeography of the Bateig area should provide further testing for this hypothesis. The ichnofacies and stacking of the Bateig Limestone differ from the classic Seilacherian model in that they reflect changes in hydraulic process and are associated with faulting and subsidence and changes in sediment supply. Recognition of the unusual ichnofabrics and their relationships provides a clear indication of the overall dynamic setting. (c) 2006 Elsevier B.V. All rights reserved.

Hydraulic modeling of runoff over a rough surface under partial inundation

This study presents a numerical method to derive the Darcy- Weisbach friction coefficient for overland flow under partial inundation of surface roughness. To better account for the variable influence of roughness with varying levels of emergence, we model the flow over a network which evolves as the free surface rises. This network is constructed using a height numerical map, based on surface roughness data, and a discrete geometry skeletonization algorithm. By applying a hydraulic model to the flows through this network, local heads, velocities, and Froude and Reynolds numbers over the surface can be estimated. These quantities enable us to analyze the flow and ultimately to derive a bulk friction factor for flow over the entire surface which takes into account local variations in flow quantities. Results demonstrate that although the flow is laminar, head losses are chiefly inertial because of local flow disturbances. The results also emphasize that for conditions of partial inundation, flow resistance varies nonmonotonically but does generally increase with progressive roughness inundation.

Hydrolysis of N2O5 on submicron sulfuric acid aerosols

The kinetics of reactive uptake of gaseous N2O5 on submicron sulfuric acid aerosol particles has been investigated using a laminar flow reactor coupled with a differential mobility analyzer (DMA) to characterize the aerosol. The particles were generated by homogeneous nucleation of SO3/H2O mixtures. In the H2SO4 concentration range 26.3−64.5 wt % the uptake coefficient was γ = 0.033 ± 0.004, independent of acid strength. For an acid strength of 45 wt % γ was found to decrease with increasing temperature over the range 263−298 K. From this, temperature dependence values of −115 ± 30 kJ/mol and −25.5 ± 8.4 J/K mol were determined for the changes in enthalpy and entropy of the uptake process, respectively. The results are consistent with a previous model of N2O5 hydrolysis involving both a direct and an acid catalyzed mechanism, with uptake under the experimental conditions limited by mass accommodation.

Hydrolysis of N2O5 on sub-micron mineral salt aerosols

The kinetics of reactive uptake of gaseous N2O5 on sub-micron aerosol particles composed of aqueous ammonium sulfate, ammonium hydrogensulfate and sodium nitrate has been investigated. Uptake was measured in a laminar flow reactor, coupled with a differential mobility analyser (DMA) to obtain the aerosol size distribution, with N2O5 detection using NO chemiluminescence. FTIR spectroscopy was used to obtain information about the composition and water content of the aerosol particles under the conditions used in the kinetic measurements. The aerosols were generated by the nebulisation of aqueous salt solutions. The uptake coefficient on the sulfate salts was in the range [gamma]=0.0015 to 0.033 depending on temperature, humidity and phase of the aerosol. On sodium nitrate aerosols the values were much lower, [gamma]<0.001, confirming the inhibition of N2O5 hydrolysis by nitrate ions. At high humidity (>50% r.h.) the uptake coefficient on liquid sulfate aerosols is independent of water content, but at lower humidity, especially below the efflorescence point, the reactivity of the aerosol declines, correlating with the lower water content. The lower uptake rate on solid aerosols may be due to limitations imposed by the liquid volume in the particles. Uptake on sulfate aerosols showed a negative temperature dependence at T>290 K but no significant temperature dependence at lower temperatures. The results are generally consistent with previous models of N2O5 hydrolysis where the reactive intermediate is NO2+ produced by autoionisation of nitrogen pentoxide in the condensed phase.

Deposition of charged inhaled aerosols with transient airflow in sequential lung airway model

Transport and deposition of charged inhaled aerosols in double planar bifurcation representing generation three to five of human respiratory system has been studied under a light activity breathing condition. Both steady and oscillatory laminar inhalation airflow is considered. Particle trajectories are calculated using a Lagrangian reference frame, which is dominated by the fluid force driven by airflow, gravity force and electrostatic forces (both of space and image charge forces). The particle-mesh method is selected to calculate the space charge force. This numerical study investigates the deposition efficiency in the three-dimensional model under various particle sizes, charge values, and inlet particle distribution. Numerical results indicate that particles carrying an adequate level of charge can improve deposition efficiency in the airway model.

Investigation of flux in flat-plate modules for membrane distillation

A theoretical model for predicting the behaviour of membrane distillation by incorporating mass and heat transfer equations has been used to find permeate fluxes, and has been validated experimentally. The model accurately predicts mass and heat transfer. The main work studied the effect of module design using a flat-plate module in laminar flow conditions. Areas of investigation included the use of channels across the membrane surface, decreasing the available membrane surface area, and widening the inlet and outlet channels. The work showed that widening the channels increased the flux. Increased flux was also obtained by the use of channels on the permeate side, though not on the feed side.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Classification of cortical microcircuits based on micro-electrode-array data from slices of rat barrel cortex

The bewildering complexity of cortical microcircuits at the single cell level gives rise to surprisingly robust emergent activity patterns at the level of laminar and columnar local field potentials (LFPs) in response to targeted local stimuli. Here we report the results of our multivariate data-analytic approach based on simultaneous multi-site recordings using micro-electrode-array chips for investigation of the microcircuitary of rat somatosensory (barrel) cortex. We find high repeatability of stimulus-induced responses, and typical spatial distributions of LFP responses to stimuli in supragranular, granular, and infragranular layers, where the last form a particularly distinct class. Population spikes appear to travel with about 33 cm/s from granular to infragranular layers. Responses within barrel related columns have different profiles than those in neighbouring columns to the left or interchangeably to the right. Variations between slices occur, but can be minimized by strictly obeying controlled experimental protocols. Cluster analysis on normalized recordings indicates specific spatial distributions of time series reflecting the location of sources and sinks independent of the stimulus layer. Although the precise correspondences between single cell activity and LFPs are still far from clear, a sophisticated neuroinformatics approach in combination with multi-site LFP recordings in the standardized slice preparation is suitable for comparing normal conditions to genetically or pharmacologically altered situations based on real cortical microcircuitry.

Temporal coupling between stimulus-evoked neural activity and hemodynamic responses from individual cortical columns

Using previously published data from the whisker barrel cortex of anesthetized rodents (Berwick et al 2008 J. Neurophysiol. 99 787–98) we investigated whether highly spatially localized stimulus-evoked cortical hemodynamics responses displayed a linear time-invariant (LTI) relationship with neural activity. Presentation of stimuli to individual whiskers of 2 s and 16 s durations produced hemodynamics and neural activity spatially localized to individual cortical columns. Two-dimensional optical imaging spectroscopy (2D-OIS) measured hemoglobin responses, while multi-laminar electrophysiology recorded neural activity. Hemoglobin responses to 2 s stimuli were deconvolved with underlying evoked neural activity to estimate impulse response functions which were then convolved with neural activity evoked by 16 s stimuli to generate predictions of hemodynamic responses. An LTI system more adequately described the temporal neuro-hemodynamics coupling relationship for these spatially localized sensory stimuli than in previous studies that activated the entire whisker cortex. An inability to predict the magnitude of an initial 'peak' in the total and oxy- hemoglobin responses was alleviated when excluding responses influenced by overlying arterial components. However, this did not improve estimation of the hemodynamic responses return to baseline post-stimulus cessation.

The resting-state neurovascular coupling relationship: rapid changes in spontaneous neural activity in the somatosensory cortex are associated with haemodynamic fluctuations that resemble stimulus-evoked haemodynamics

Although promise exists for patterns of resting-state blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) brain connectivity to be used as biomarkers of early brain pathology, a full understanding of the nature of the relationship between neural activity and spontaneous fMRI BOLD fluctuations is required before such data can be correctly interpreted. To investigate this issue, we combined electrophysiological recordings of rapid changes in multi-laminar local field potentials from the somatosensory cortex of anaesthetized rats with concurrent two-dimensional optical imaging spectroscopy measurements of resting-state haemodynamics that underlie fluctuations in the BOLD fMRI signal. After neural ‘events’ were identified, their time points served to indicate the start of an epoch in the accompanying haemodynamic fluctuations. Multiple epochs for both neural ‘events’ and the accompanying haemodynamic fluctuations were averaged. We found that the averaged epochs of resting-state haemodynamic fluctuations taken after neural ‘events’ closely resembled the temporal profile of stimulus-evoked cortical haemodynamics. Furthermore, we were able to demonstrate that averaged epochs of resting-state haemodynamic fluctuations resembling the temporal profile of stimulus-evoked haemodynamics could also be found after peaks in neural activity filtered into specific electroencephalographic frequency bands (theta, alpha, beta, and gamma). This technique allows investigation of resting-state neurovascular coupling using methodologies that are directly comparable to that developed for investigating stimulus-evoked neurovascular responses.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

The role of anomalous SST and surface fluxes over the Southeastern North Atlantic in the explosive development of windstorm Xynthia

In late February 2010 the extraordinary windstorm Xynthia crossed over Southwestern and Central Europe and caused severe damage, affecting particularly the Spanish and French Atlantic coasts. The storm was embedded in uncommon large-scale atmospheric and boundary conditions prior to and during its development, namely enhanced sea surface temperatures (SST) within the low-level entrainment zone of air masses, an unusual southerly position of the polar jet stream, and a remarkable split jet structure in the upper troposphere. To analyse the processes that led to the rapid intensification of this exceptional storm originating close to the subtropics (30°N), the sensitivity of the cyclone intensification to latent heat release is determined using the regional climate model COSMO-CLM forced with ERA-Interim data. A control simulation with observed SST shows that moist and warm air masses originating from the subtropical North Atlantic were involved in the cyclogenesis process and led to the formation of a vertical tower with high values of potential vorticity (PV). Sensitivity studies with reduced SST or increased laminar boundary roughness for heat led to reduced surface latent heat fluxes. This induced both a weaker and partly retarded development of the cyclone and a weakening of the PV-tower together with reduced diabatic heating rates, particularly at lower and mid levels. We infer that diabatic processes played a crucial role during the phase of rapid deepening of Xynthia and thus to its intensity over the Southeastern North Atlantic. We suggest that windstorms like Xynthia may occur more frequently under future climate conditions due to the warming SSTs and potentially enhanced latent heat release, thus increasing the windstorm risk for Southwestern Europe.

A gradual depth-dependent change of connectivity features of supragranular pyramidal cells in rat barrel cortex

Recent experimental evidence suggests a finer genetic, structural and functional subdivision of the layers which form a cortical column. The classical layer II/III (LII/III) of rodent neocortex integrates ascending sensory information with contextual cortical information for behavioral read-out. We systematically investigated to which extent regular-spiking supragranular pyramidal neurons, located at different depths within the cortex, show different input-output connectivity patterns. Combining glutamate-uncaging with whole-cell recordings and biocytin filling, we revealed a novel cellular organization of LII/III: (i) “Lower LII/III” pyramidal cells receive a very strong excitatory input from lemniscal LIV and much fewer inputs from paralemniscal LVa. They project to all layers of the home column, including a feedback projection to LIV whereas transcolumnar projections are relatively sparse. (ii) “Upper LII/III” pyramidal cells also receive their strongest input from LIV, but in addition, a very strong and dense excitatory input from LVa. They project extensively to LII/III as well as LVa and Vb of their home and neighboring columns, (iii) “Middle LII/III” pyramidal cell show an intermediate connectivity phenotype that stands in many ways in-between the features described for lower versus upper LII/III. “Lower LII/III” intracolumnarly segregates and transcolumnarly integrates lemniscal information whereas “upper LII/III” seems to integrate lemniscal with paralemniscal information. This suggests a finegrained functional subdivision of the supragranular compartment containing multiple circuits without any obvious cytoarchitectonic, other structural or functional correlate of a laminar border in rodent barrel cortex.