On the separation of gravitation and inertia and the determination of the relativistic gravity field in the case of free motion

Summary The authors explored the possibility of separating gravitation from inertia in the frame of general relativity. The Riemann tensor is intimately related with gravitational fields and has nothing to do with inertial effects. One can judge the existence or nonexistence of a gravitational field according as the Riemann tensor does not vanish or vanishes. In the free fall case, by using a gradiometer on a satellite, gravitational effects can be separated from inertia completely. Furthermore, the authors put forward a general method of determining the relativistic gravity field by using gradiometers mounted on satellites. At the same time the following two statements are proved: in the case of using gradiometers on a satellite, with some kind of approximation the Riemann tensorR can be found; in the case of free motion, if the measured Riemannian componentsR _(i0j0) are equal to zero, the Riemann tensorR equals zero.     

Using embodied HANPP to analyze teleconnections in the global land system: Conceptual considerations

Geografisk Tidsskrift—Danish Journal of Geography 109(2):119–130, 2009

In our rapidly globalizing world economy activities in one region have increasingly important effects on ecological, economic or social processes elsewhere, an effect which we here denote as ‘teleconnections’ between different regions. Biomass trade, one of the causes behind such teleconnections, is currently growing exponentially. Integrated analyses of changes in the global land system are high on the agenda of sustainability science, but a methodological framework for a consistent allocation of environmental burdens related to the consumption and production of biomass between regions has not been put forth to date. The concept of the ‘embodied human appropriation of net primary production’ (abbreviated ‘embodied HANPP’ or ‘eHANPP’) allows for the assessment of the ‘upstream’ effects on ecosystem energetics associated with a particular level of biomass consumption or with a given biomass-based product. This concept is based on HANPP and its two components: (1) productivity changes resulting from land conversion (ΔNPP_LC), and (2) harvest of biomass in ecosystems (NPP_h). HANPP, defined as the sum of ΔANPP_LC and NPP_h in any given territory, is indicative of the intensity with which humans use the land for their purposes. eHANPP is defined as the NPP appropriated in the course of biomass production, encompassing losses along the production chain as well as productivity changes induced through land conversion or harvest. By making the pressure exerted on ecosystems associated with imports and exports visible, eHANPP allows for the analysis of teleconnections between producing and consuming regions. This article puts forward the eHANPP concept, illustrates its utility for integrated socioecological land-change research based on top-down data on global HANPP and biomass consumption, and discusses the possibilities and challenges related to its quantification in bottom-up approaches.     

Modification of air flow over an escarpment — Results from the Hjardemål experiment

Mean flow, turbulence, and surface pressure measurements over an escarpment are presented. The speed-up in the mean wind field shows the known dependence on stratification. Cross-sections of the standard deviation of horizontal and vertical wind components and of the friction velocity are derived from the data and compare favorably with the numerical model of Zeman and Jensen (1987). The modification of turbulent power spectra at intermediate frequencies can be explained by rapid distortion theory. At very low frequencies, there is a quasi-stationary response to the disturbance. Except for speed-up and standard deviations of the wind components, which are also shown for downslope wind, all results in this paper refer to upslope winds.An analysis of the vertical momentum flux reveals that upstream of the escarpment, most of the flux is transported in sweeps of fast, sinking motion to the ground. Downstream of the escarpment, ejections of slow, rising motion dominate the turbulent transport.     

Intra‐event scale bar–bank interactions and their role in channel widening

Channel bars and banks strongly affect the morphology of both braided and meandering rivers. Accordingly, bar formation and bank erosion processes have been greatly explored. There is, however, a lack of investigations addressing the interactions between bed and bank morphodynamics, especially over short timescales. One major implication of this gap is that the processes leading to the repeated accretion of mid‐channel bars and associated widenings remain unsolved. In a restored section of the Drau River, a gravel‐bed river in Austria, mid‐channel bars have developed in a widening channel. During mean flow conditions, the bars divert the flow towards the banks. One channel section exhibited both an actively retreating bank and an expanding mid‐channel bar, and was selected to investigate the morphodynamic processes involved in bar accretion and channel widening at the intra‐event timescale. We repeatedly surveyed riverbed and riverbank topography, monitored riverbank hydrology and mounted a time‐lapse camera for continuous observation of riverbank erosion processes during four flow events. The mid‐channel bar was shown to accrete when it was submerged during flood events, which at the subsequent flow diversion during lower discharges narrowed the branch along the bank and increased the water surface elevation upstream from the riffle, which constituted the inlet into the branch. These changes of bed topography accelerated the flow along the bank and triggered bank failures up to 20 days after the flood events. Four analysed flow events exhibited a total bar expansion from initially 126 m² to 295 m², while bank retreat was 6 m at the apex of the branch. The results revealed the forcing role of bar accretion in channel widening and highlighted the importance of intra‐event scale bed morphodynamics for bank erosion, which were summarized in a conceptual model of the observed bar–bank interactions. Copyright © 2015 John Wiley & Sons, Ltd.     

Validating a turbulence closure against estuarine microstructure measurements

A simple k–ε turbulence closure is introduced which has no stability functions but instead a Richardson number-dependent turbulent Prandtl number. Its free parameters are determined in a comparison with microstructure observations from a stratified and sheared tidal estuary and laboratory measurements. The closure is able to simulate observed turbulent dissipation rates (ε) and turbulent length scales (l_th) in regions of strong mean shear and small gradient Richardson number (R_g) to within factors of 2–3. It fails in regions of small shear and large R_g, presumably because of the dominance of internal wave-driven mixing. Additional simulations with a k–ε closure with stability functions taken from Canuto et al. [Canuto, V.M., Howard, A., Cheng, Y., Dubovikov, M.S., 2001. Ocean turbulence I: one-point closure model. Momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413–1426] and with the closure of Baumert and Peters [Baumert, H., Peters, H., 2004. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34, 505–512] show poor performance. Establishing a valid 1:1 comparison of simulated and observed ε and l_th requires nudging the model velocity and density toward observed values because free model integrations quickly diverge from the observations. Steady state gradient Richardson numbers are constrained to a range of 0.18–0.25, while flux Richardson numbers are constrained to the range of 0.1–0.22. The closure output is rather insensitive to such parameter variations. The simulations are sensitive, however, to the treatment of the observed velocity and density used to nudge the model. Good closure performance requires averaging the measured tidal flow over about an hour, a time scale for which conventional numerical models of estuarine circulations should be able to match observed shears. In the closure simulations the TKE balance stays close to a production–dissipation balance. The time rate of change and vertical diffusion of TKE are small, of the same order of magnitude, and vary in magnitude relative to each other systematically across the water column.