Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different “order parameters” including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local–nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Simulation of Direct Contact Condensation Using Large Scale Interface Multifluid Model

The Large Scale Interface (LSI) model of the Euler-Euler method in STAR-CCM+ is extended to simulate two-phase flow with phase change. This extended methodology is used to simulate direct contact condensation (DCC) of steam in a hot leg when cold water is injected by emergency core cooling system to remove the residual heat. The case corresponds an experimental study conducted at Hungarian Atomic Energy Research Institute KFKI using the PMK-2 device. Out of the several experiments reported for this scenario, the one experiment considered in this work corresponds to a case without the water hammer phenomena. It was found that the LSI model is able to capture core physics of direct contact condensation during steam-water counter-current flow in a pipe. The model could capture entrapment of steam between the interface and its subsequent rapid condensation. The role of the relaxation time-scale of the large interface drag and the turbulence damping at interface is also studied.

Spatiotemporal Long-Range Persistence in Earth’s Temperature Field: Analysis of Stochastic–Diffusive Energy Balance Models

A two-dimensional stochastic–diffusive energy balance model (EBM) formulated on a sphere by G. R. North et al. is explored and generalized. Instantaneous and frequency-dependent spatial autocorrelation functions and local temporal power spectral densities are computed for local sites and for spatially averaged surface temperature signals up to the global scale. On time scales up to the relaxation time scale given by the effective heat capacities of the ocean mixed layer and land surface, respectively, scaling features are obtained that are reminiscent of what can be derived from the observed temperature field. On longer time scales, however, the EBM predicts a transition to a white-noise scaling, which is not reflected in the observed records. A fractional generalization, which can be considered as a spatial generalization of the zero-dimensional, long-memory EBM of M. Rypdal and K. Rypdal, is proposed and explored. It is demonstrated that this generalized model describes qualitatively the main correlation characteristics of the temperature field reported in the literature and those derived herein from 500-yr-long control simulations of the NorESM Earth system model. A further generalization of the model, to include long-term persistence in the stochastic forcing, is also discussed.

Relation between the 100-hPa Heat Flux and Stratospheric Potential Vorticity

It is shown that a quantitative relation exists between the stratospheric polar cap potential vorticity and the 100-hPa eddy heat flux. A difference in potential vorticity between years is found to be linearly related to the flux difference integrated over time, taking into account a decrease in relaxation time scale with height in the atmosphere. This relation (the PV–flux relation) is then applied to the 100-hPa flux difference between 2008/09 and the climatology (1989–2008) to obtain a prediction of the polar cap potential vorticity difference between the 2008/09 winter and the climatology. A prediction of the 2008/09 polar cap potential vorticity is obtained by adding this potential vorticity difference to the climatological potential vorticity. The observed polar cap potential vorticity for 2008/09 shows a large and abrupt change in the potential vorticity in midwinter, related to the occurrence of a major sudden stratospheric warming in January 2009; this is also captured by the potential vorticity predicted from the 100-hPa flux and the PV–flux relation. The results of the mean PV–flux relation show that, on average, about 50% of the interannual variability in the state of the Northern Hemisphere stratosphere is determined by the variations in the 100-hPa heat flux. This explained variance can be as large as 80% for more severe events, as demonstrated for the 2009 major warming.

Sensitivity of the simulated precipitation to changes in convective relaxation time scale

The paper describes the sensitivity of the simulated precipitation to changes in convective relaxation time scale (TAU) of Zhang and McFarlane (ZM) cumulus parameterization, in NCAR-Community Atmosphere Model version 3 (CAM3). In the default configuration of the model, the prescribed value of TAU, a characteristic time scale with which convective available potential energy (CAPE) is removed at an exponential rate by convection, is assumed to be 1 h. However, some recent observational findings suggest that, it is larger by around one order of magnitude. In order to explore the sensitivity of the model simulation to TAU, two model frameworks have been used, namely, aqua-planet and actual-planet configurations. Numerical integrations have been carried out by using different values of TAU, and its effect on simulated precipitation has been analyzed. The aqua-planet simulations reveal that when TAU increases, rate of deep convective precipitation (DCP) decreases and this leads to an accumulation of convective instability in the atmosphere. Consequently, the moisture content in the lower- and mid- troposphere increases. On the other hand, the shallow convective precipitation (SCP) and large-scale precipitation (LSP) intensify, predominantly the SCP, and thus capping the accumulation of convective instability in the atmosphere. The total precipitation (TP) remains approximately constant, but the proportion of the three components changes significantly, which in turn alters the vertical distribution of total precipitation production. The vertical structure of moist heating changes from a vertically extended profile to a bottom heavy profile, with the increase of TAU. Altitude of the maximum vertical velocity shifts from upper troposphere to lower troposphere. Similar response was seen in the actual-planet simulations. With an increase in TAU from 1 h to 8 h, there was a significant improvement in the simulation of the seasonal mean precipitation. The fraction of deep convective precipitation was in much better agreement with satellite observations.

Spectral properties and universal behaviour of advecting–diffusing scalar fields in finite-length channels

This paper analyses the relaxation towards the steady state of an advecting–diffusing field in a finite-length channel. The dominant eigenvalue, −-ΛF, of the advection–diffusion operator provides the slowest relaxation time scale for achieving steady state in open flow devices. We focus on parallel flows and analyse how ΛF depends on the velocity profile and the molecular diffusivity. As a result of the universal localization features of the eigenfunction associated with ΛF, we find that ΛF can be predicted analytically based on the local behaviour of the velocity profile near the stagnation points. Microfluidic applications of the theory are also addressed.