Energetics of a symmetric circulation including momentum constraints

A theory of available potential energy (APE) for symmetric circulations, which includes momentum constraints, is presented. The theory is a generalization of the classical theory of APE, which includes only thermal constraints on the circulation. Physically, centrifugal potential energy is included along with gravitational potential energy. The generalization relies on the Hamiltonian structure of the conservative dynamics, although (as with classical APE) it still defines the energetics in a nonconservative framework. It follows that the theory is exact at finite amplitude, has a local form, and can be applied to a variety of fluid models. It is applied here to the f -plane Boussinesq equations. It is shown that, by including momentum constraints, the APE of a symmetrically stable flow is zero, while the energetics of a mechanically driven symmetric circulation properly reflect its causality.

Hamiltonian geophysical fluid dynamics

Hamiltonian dynamics describes the evolution of conservative physical systems. Originally developed as a generalization of Newtonian mechanics, describing gravitationally driven motion from the simple pendulum to celestial mechanics, it also applies to such diverse areas of physics as quantum mechanics, quantum field theory, statistical mechanics, electromagnetism, and optics – in short, to any physical system for which dissipation is negligible. Dynamical meteorology consists of the fundamental laws of physics, including Newton’s second law. For many purposes, diabatic and viscous processes can be neglected and the equations are then conservative. (For example, in idealized modeling studies, dissipation is often only present for numerical reasons and is kept as small as possible.) In such cases dynamical meteorology obeys Hamiltonian dynamics. Even when nonconservative processes are not negligible, it often turns out that separate analysis of the conservative dynamics, which fully describes the nonlinear interactions, is essential for an understanding of the complete system, and the Hamiltonian description can play a useful role in this respect. Energy budgets and momentum transfer by waves are but two examples.

Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence

We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form νμ(−Δ)μ. By “monoscale-like” we mean that the forcing is applied over a finite range of wavenumbers kmin≤k≤kmax, and that the ratio of enstrophy injection η≥0 to energy injection ε≥0 is bounded by kmin2ε≤η≤kmax2ε. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for μ≥0 the asymptotic behaviour satisfies ∥u∥12≤kmax2∥u∥2, where ∥u∥2 and ∥u∥12 are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier–Stokes turbulence (μ=1), the time-mean enstrophy dissipation rate is bounded from above by 2ν1kmax2. These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier–Stokes turbulence (μ=1) when it is forced in this manner. Inclusion of Ekman drag (μ=0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified −3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (μ<0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing.

The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

On the 'downward control' of extratropical diabatic circulations by eddy-induced mean zonal forces

The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force F̄, conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force F̄ may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the F̄ distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governing the average rate at which photochemical products like ozone become available for folding into, or otherwise descending into, the extratropical troposphere. The dynamical facts expressed by the principle are also relevant, for instance, to understanding the seasonal-mean rate of upwelling of water vapor to the summer mesopause, and the interhemispheric differences in stratospheric tracer transport. The robustness of the principle is examined when F̄ is time-dependent. For a global-scale, zonally symmetric diabatic circulation with a Brewer-Dobson-like horizontal structure given by the second zonally symmetric Hough mode, with Rossby height HR = 13 km in an isothermal atmosphere with density scale height H = 7 km, the vertical partitioning of the unsteady part of the mass circulation caused by fluctuations in F̄ confined to a shallow layer LF̄ is always at least 84% downward. It is 90% downward when the force fluctuates sinusoidally on twice the radiative relaxation timescale and 95% if five times slower. The time-dependent adjustment when F̄ is changed suddenly is elucidated, extending the work of Dickinson (1968), when the atmosphere is unbounded above and below. Above the forcing, the adjustment is characterized by decay of the meridional mass circulation cell at a rate proportional to the radiative relaxation rate τr−1 divided by {1 + (4H2/HR2)}. This decay is related to the boundedness of the angular momentum that can be taken up by the finite mass of air above LF̄ without causing an ever-increasing departure from thermal wind balance. Below the forcing, the meridional mass circulation cell penetrates downward at a speed τr−1 HR2/H. For the second Hough mode, the time for downward penetration through one density scale height is about 6 days if the radiative relaxation time is 20 days, the latter being representative of the lower stratosphere. At any given altitude, a steady state is approached. The effect of a rigid lower boundary on the time-dependent adjustment is also considered. If a frictional planetary boundary layer is present then a steady state is ultimately approached everywhere, with the mass circulation extending downward from LF̄ and closing via the boundary layer. Satellite observations of temperature and ozone are used in conjunction with a radiative transfer scheme to estimate the altitudes from which the lower stratospheric diabatic vertical velocity is controlled by the effective F̄ in the real atmosphere. The data appear to indicate that about 80% of the effective control is usually exerted from below 40 km but with significant exceptions up to 70 km (in the high latitude southern hemispheric winter). The implications for numerical modelling of chemical transport are noted.

Tracking the momentum flux of a CME and quantifying its influence on geomagnetically induced currents at Earth

We investigate a coronal mass ejection (CME) propagating toward Earth on 29 March 2011. This event is specifically chosen for its predominately northward directed magnetic field, so that the influence from the momentum flux onto Earth can be isolated. We focus our study on understanding how a small Earth-directed segment propagates. Mass images are created from the white-light cameras onboard STEREO which are also converted into mass height-time maps (mass J-maps). The mass tracks on these J-maps correspond to the sheath region between the CME and its associated shock front as detected by in situ measurements at L1. A time series of mass measurements from the STEREO COR-2A instrument is made along the Earth propagation direction. Qualitatively, this mass time series shows a remarkable resemblance to the L1 in situ density series. The in situ measurements are used as inputs into a three-dimensional (3-D) magnetospheric space weather simulation from the Community Coordinated Modeling Center. These simulations display a sudden compression of the magnetosphere from the large momentum flux at the leading edge of the CME, and predictions are made for the time derivative of the magnetic field (dB/dt) on the ground. The predicted dB/dt values were then compared with the observations from specific equatorially located ground stations and showed notable similarity. This study of the momentum of a CME from the Sun down to its influence on magnetic ground stations on Earth is presented as a preliminary proof of concept, such that future attempts may try to use remote sensing to create density and velocity time series as inputs to magnetospheric simulations.

Simulations of angular momentum evolution in wind-fed CV precursors

It is thought that the secondary stars in cataclysmic variables (CVs) may undergo a period of mass loss in the form of a wind during the evolution of the system (Mullan et al. 1992). This wind is thought to magnetically brake the secondary star with a time-scale ~ 10^8 yr (e.g. van Paradijs 1986). When the secondary’s spin has been brought close to synchronism with the orbit it is possible for tidal torques to lock the secondary in synchronous rotation.

The influence of Antarctica on the momentum budget of the southern extratropics

The antarctic plateau acts as a strong heat sink for the global climate, cooling the atmosphere and radiating energy to space. A cold dense atmospheric boundary layer is formed. Strong surface winds are formed as the boundary layer drains off the plateau. These drainage winds and the eddy fluxes necessary to maintain them are analysed in a general circulation model (GCM). The drainage flow is well represented in the GCM. The associated mean meridional circulation is analysed in isentropic coordinates. The momentum budget over Antarctica reveals a balance between the Eliassen-Palm flux convergence and the Coriolis torque exerted by the mean meridional mass flux. Both vertical and horizontal components of the Eliassen-Palm flux contribute, the vertical component being the greater.

Low-cost momentum strategies

This paper analyses the impact of trading costs on the profitability of momentum strategies in the United Kingdom and concludes that losers are more expensive to trade than winners. The observed asymmetry in the costs of trading winners and losers crucially relates to the high cost of selling loser stocks with small size and low trading volume. Since transaction costs severely impact net momentum profits, the paper defines a new low-cost relative-strength strategy by shortlisting from all winner and loser stocks those with the lowest total transaction costs. While the study severely questions the profitability of standard momentum strategies, it concludes that there is still room for momentum-based return enhancement, should asset managers decide to adopt low-cost relative-strength strategies.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Rationality and momentum in real estate investment forecasts

This study examines the rationality and momentum in forecasts for rental, capital value and total returns for the real estate investment market in the United Kingdom. In order to investigate if forecasters are affected by the general economic conditions present at the time of forecast we incorporate into the analysis Gross Domestic Product(GDP) and the Default Spread (DS). The empirical findings show high levels of momentum in the forecasts, with highly persistent forecast errors. The results also indicate that forecasters are affected by adverse conditions. This is consistent with the finding that they tend to exhibit greater forecast error when the property market is underperforming and vice-versa.

Interplanetary magnetic field control of dayside auroral activity and the transfer of momentum across the dayside magnetopause

The orientation of the Interplanetary Magnetic Field (IMF) during transient bursts of ionospheric flow and auroral activity in the dayside auroral ionosphere is studied, using data from the EISCAT radar, meridian-scanning photometers, and an all-sky TV camera, in conjunction with simultaneous observations of the interplanetary medium by the IMP-8 satellite. It is found that the ionospheric flow and auroral burst events occur regularly (mean repetition period equal to 8.3 ± 0.6 min) during an initial period of about 45 min when the IMF is continuously and strongly southward in GSM coordinates, consistent with previous observations of the occurrence of transient dayside auroral activity. However, in the subsequent 1.5 h, the IMF was predominantly northward, and only made brief excursions to a southward orientation. During this period, the mean interval between events increased to 19.2 ± 1.7 min. If it is assumed that changes in the North-South component of the IMF are aligned with the IMF vector in the ecliptic plane, the delays can be estimated between such a change impinging upon IMP-8 and the response in the cleft ionosphere within the radar field-of-view. It is found that, to within the accuracy of this computed lag, each transient ionospheric event during the period of predominantly northward IMF can be associated with a brief, isolated southward excursion of the IMF, as observed by IMP-8. From this limited period of data, we therefore suggest that transient momentum exchange between the magnetosheath and the ionosphere occurs quasi-periodically when the IMF is continuously southward, with a mean period which is strikingly similar to that for Flux Transfer Events (FTEs) at the magnetopause. During periods of otherwise northward IMF, individual momentum transfer events can be triggered by brief swings to southward IMF. Hence under the latter conditions the periodicity of the events can reflect a periodicity in the IMF, but that period will always be larger than the minimum value which occurs when the IMF is strongly and continuously southward.

Observations at the magnetopause and in the auroral ionosphere of momentum transfer from the solar wind

Recent radar studies of field-perpendicular flows in the auroral ionosphere, in conjunction with observations of the interplanetary medium immediately upstream of the Earth's bow shock, have revealed direct control of dayside convection by the Bz component of the interplanetary magnetic field (IMF). The ionospheric flows begin to respond to both northward and southward turnings of the IMF impinging upon the magnetopause after a delay of only a few minutes in the early afternoon sector, rising to about 15 minutes nearer dawn and dusk. In both the polar cap and the auroral oval, the subsequent rise and decay times are of order 5–10 minutes. We conclude there is very little convection “flywheel” effect in the dayside polar ionosphere and that only newly-opened flux tubes impart significant momentum to the ionosphere, in a relatively narrow region immediately poleward of the cusp. These findings concerning the effects of quasi-steady reconnection have important implications for any ionospheric signatures of transient reconnection which should be considerably shorter-lived than thought hitherto. In order to demonstrate the difficulty of uniquely identifying a Flux Transfer Event (FTE) in ground-based magnetometer data, we present observations of an impulsive signature, identical with that expected for an FTE if data from only one station is studied, following an observed magnetopause compression when the IMF was purely northward. We also report new radar observations of a viscous-like interaction, consistent with an origin on the flanks of the magnetotail and contributing an estimated 15–30kV to the total cross-cap potential during quiet periods.

The role of evaporating showers in the transfer of sting-jet momentum to the surface

The most damaging winds in a severe extratropical cyclone often occur just ahead of the evaporating ends of cloud filaments emanating from the so-called cloud head. These winds are associated with low-level jets (LLJs), sometimes occurring just above the boundary layer. The question then arises as to how the high momentum is transferred to the surface. An opportunity to address this question arose when the severe ‘St Jude's Day’ windstorm travelled across southern England on 28 October 2013. We have carried out a mesoanalysis of a network of 1 min resolution automatic weather stations and high-resolution Doppler radar scans from the sensitive S-band Chilbolton Advanced Meteorological Radar (CAMRa), along with satellite and radar network imagery and numerical weather prediction products. We show that, although the damaging winds occurred in a relatively dry region of the cyclone, there was evidence within the LLJ of abundant precipitation residues from shallow convective clouds that were evaporating in a localized region of descent. We find that pockets of high momentum were transported towards the surface by the few remaining actively precipitating convective clouds within the LLJ and also by precipitation-free convection in the boundary layer that was able to entrain evaporatively cooled air from the LLJ. The boundary-layer convection was organized in along-wind rolls separated by 500 to about 3000 m, the spacing varying according to the vertical extent of the convection. The spacing was greatest where the strongest winds penetrated to the surface. A run with a medium-resolution version of the Weather Research and Forecasting (WRF) model was able to reproduce the properties of the observed LLJ. It confirmed the LLJ to be a sting jet, which descended over the leading edge of a weaker cold-conveyor-belt jet.

Hydrodynamics with spin angular momentum from systematic coarse graining: a tutorial example

The derivation of time evolution equations for slow collective variables starting from a micro- scopic model system is demonstrated for the tutorial example of the classical, two-dimensional XY model. Projection operator techniques are used within a nonequilibrium thermodynamics framework together with molecular simulations in order to establish the building blocks of the hydrodynamics equations: Poisson brackets that determine the deterministic drift, the driving forces from the macroscopic free energy and the friction matrix. The approach is rather general and can be applied for deriving the equations of slow variables for a broad variety of systems.