Thermodynamic derivation and use of a nonequilibrium canonical ensemble

A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium canonical distribution implies some important results from nonequilibrium thermodynamics, specifically, the fluctuation theorem and the Jarzynski-equality.Comment: 4 pages, 0 figure

The chaos machine: analogue computing rediscovered (1)

Analogue computers provide actual rather than virtual representations of model systems. They are powerful and engaging computing machines that are cheap and simple to build. This two-part Retronics article helps you build (and understand!) your own analogue computer to simulate the Lorenz butterfly that's become iconic for Chaos theory

Accurate, simple equation for saturated vapour pressure over water and ice

We present and assess a simple equation for saturated vapour pressure over water and ice. The equation does not rely on an explicit integration of the Clausius–Clapeyron equation, but instead uses the equality of the Gibbs functions of the vapour and the liquid or ice in equilibrium. The resulting equation is simple, physically consistent with standard thermodynamic assumptions, uses only basic physical parameters, and is at least as accurate as commonly used empirical fits. It is further shown that the finite volume of liquid water has a negligible effect on the vapour pressure. The main variation from accurate tabulated data results from the variation of vapour and liquid isobaric heat capacities. Nevertheless, it is shown that, for the purpose of accurate calculation of saturated vapour pressure, this can usually be ignored

Latitudinal storm track shift in a reduced two-level model of the atmosphere

The eddy-driven jet stream and storm tracks in the mid-latitude atmosphere are known to shift in latitude on various timescales, but the physical processes that cause these shifts are still unclear. In this study, we introduce a minimal dynamical system derived from the classical Phillips two-level model with the goal of elucidating the essential mechanisms responsible for the interaction between eddies and mean flow. Specifically, we aim to understand the link between the structure of the eddies and the shift of the latitudinal maximum of the zonal flow. By varying the horizontal shape of the eddies, we find three distinct dynamical regimes whose occurrence depends on the intensity of the external baroclinic forcing: a purely zonal flow, a barotropic eddy regime with net poleward momentum flux, and a baroclinic eddy regime with both net poleward momentum and temperature flux. For weak baroclinic forcing, the classical zonal flow solution with latitudinal maximum at the centre of the beta-channel is found. For strong forcing, if eddies are southwest-northeast tilted and zonally elongated, the system is in the baroclinic eddy regime, resulting in a poleward shift of the jet. The intermediate barotropic eddy regime also features a poleward shifted jet, yet with eddies structurally distinct from the baroclinic regime. Changing the parameters yields transitions between the regimes that can be either continuous or discontinuous in terms of the properties of the atmosphere. The findings of this study also provide insights into the properties of the storm track change between the jet entrance and jet exit regions of the North Atlantic.Comment: 15 pages, 4 figure

The lifecycle of the North Atlantic storm track

The North Atlantic eddy-driven jet exhibits latitudinal variability, with evidence of three preferred latitudinal locations: south, middle and north. Here we examine the drivers of this variability and the variability of the associated storm track. We investigate the changes in the storm track characteristics for the three jet locations, and propose a mechanism by which enhanced storm track activity, as measured by upstream heat flux, is responsible for cyclical downstream latitudinal shifts in the jet. This mechanism is based on a nonlinear oscillator relationship between the enhanced meridional temperature gradient (and thus baroclinicity) and the meridional high-frequency (periods of shorter than 10 days) eddy heat flux. Such oscillations in baroclinicity and heat flux induce variability in eddy anisotropy which is associated with the changes in the dominant type of wave breaking and a different latitudinal deflection of the jet. Our results suggest that high heat flux is conducive to a northward deflection of the jet, whereas low heat flux is conducive to a more zonal jet. This jet deflecting effect was found to operate most prominently downstream of the storm track maximum, while the storm track and the jet remain anchored at a fixed latitudinal location at the beginning of the storm track. These cyclical changes in storm track characteristics can be viewed as different stages of the storm track’s spatio-temporal lifecycle

Baroclinic adjustment and dissipative control of storm tracks

The steady-state response of a mid-latitude storm track to large-scale extratropical thermal forcing and eddy friction is investigated in a dry general circulation model with a zonally symmetric forcing. A two-way equilibration is found between the relative responses of the mean baroclinicity and baroclinic eddy intensity, whereby mean baroclinicity responds more strongly to eddy friction whereas eddy intensity responds more strongly to the thermal forcing of baroclinicity. These seemingly counter-intuitive responses are reconciled using the steady state of a predator-prey relationship between baroclinicity and eddy intensity. This relationship provides additional support for the well studied mechanism of baroclinic adjustment in the Earth’s atmosphere, as well as providing a new mechanism whereby eddy dissipation controls the large-scale thermal structure of a baroclinically unstable atmosphere. It is argued that these two mechanisms of baroclinic adjustment and dissipative control should be used in tandem when considering storm track equilibration

Eddy saturation in a reduced two-level model of the atmosphere

Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. Here we present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips’ classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment

The implications of an idealised large-scale circulation for mechanical work done by tropical convection

A thermodynamic analysis is presented of an overturning circulation simulated by two cloud resolving models, coupled by a weak temperature gradient parametrisation. Taken together, they represent two separated regions over different sea surface temperatures, and the coupling represents an idealised large-scale circulation such as the Walker circulation. It is demonstrated that a thermodynamic budget linking net heat input to the generation of mechanical energy can be partitioned into contributions from the large-scale interaction between the two regions, as represented by the weak temperature gradient approximation, and from convective motions in the active warm region and the suppressed cool region. Model results imply that such thermodynamic diagnostics for the aggregate system are barely affected by the strength of the coupling, even its introduction, or by the SST contrast between the regions. This indicates that the weak temperature gradient parametrisation does not introduce anomalous thermodynamic behaviour. We find that the vertical kinetic energy associated with the large-scale circulation is more than three orders of magnitude smaller than the typical vertical kinetic energy in each region. However, even with very weak coupling circulations, the contrast between the thermodynamic budget terms for the suppressed and active regions is strong and is relatively insensitive to the degree of the coupling. Additionally, scaling arguments are developed for the relative values of the terms in the mechanical energy budget

Precipitation modification by ionization

Rainfall is hypothesised to be influenced by droplet charge, which is related to the global circuit current flowing through clouds. This is tested through examining a major global circuit current increase following release of artificial radioactivity. Significant changes occurred in daily rainfall distribution in the Shetland Islands, away from pollution. Daily rainfall changed by 24%, and local cloud optically thickened, within the nuclear weapons test period. This supports expectations of electrically induced microphysical changes in liquid water clouds from additional ionisation