scholarly journals On the validity of single-parcel energetics to assess the importance of internal energy and compressibility effects in stratified fluids

2015 ◽  
Vol 767 ◽  
Author(s):  
Rémi Tailleux
Keyword(s):  
Potential Energy ◽  
Internal Energy ◽  
Speed Of Sound ◽  
Mass Conservation ◽  
Scale Height ◽  
Lapse Rate ◽  
Gravitational Acceleration ◽  
Relative Importance ◽  
Global Energy Budget ◽  
Compressibility Effects

AbstractIt is often assumed on the basis of single-parcel energetics that compressible effects and conversions with internal energy are negligible whenever typical displacements of fluid parcels are small relative to the scale height of the fluid (defined as the ratio of the squared speed of sound to the gravitational acceleration). This paper shows that the above approach is flawed, however, and that a correct assessment of compressible effects and internal energy conversions requires the consideration of the energetics of at least two parcels or, more generally, of mass-conserving parcel rearrangements. As a consequence, it is shown that it is the adiabatic lapse rate and its derivative with respect to pressure, rather than the scale height, that controls the relative importance of compressible effects and internal energy conversions when considering the global energy budget of a stratified fluid. Only when mass conservation is properly accounted for is it possible to explain why the available internal energy can account for up to 40 % of the total available potential energy in the oceans. This is considerably larger than the prediction of single-parcel energetics, according to which this number should be no more than approximately 2 %.

Photochemistry of van der Waals Complexes and Small Clusters

1996 ◽  
Author(s):  
C. Jouvet ◽  
D. Solgadi
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Internal Energy ◽  
Energy Surface ◽  
Van Der Waals ◽  
Van Der Waals Complexes ◽  
Small Subset ◽  
Energy Effect ◽  
Precise Control

In a chemical reaction, the shape of the potential energy surface (PES) dictates the reaction rate and energy disposal in the products. Not only does the dynamics depend crucially upon the features of the surface, but, ultimately one seeks to influence the course of the reaction by preparing selectively certain regions of the surface. For harpooning reactions, the propensity rules for energy disposal in the products (influence of the entrance kinetic energy, effect of the early or late barrier) have been established by Polanyi (1972) and have been used later as guidelines. Here, the surface may easily be modeled in simple terms using long-range electrostatic interaction in the entrance valley. There was, then, need of an experimental method which allows the possibility of observing directly the characteristic regions of this potential energy surface, but also to investigate precisely the surface in other types of reaction. The study of the reactivity of van der Waals complexes is intended to fulfil this purpose. In classical experiments, the surface is obtained by inversion of the experimental data which are differential cross sections and internal energy distribution of the products. This procedure is difficult and not unambiguous. The first step is to determine the correlation between the entrance channel's parameters (kinetic energy, internal energy, angular momentum) and the final states of the products (kinetic energy, internal energy, angular distribution). This requires a precise control of the entrance channel. Therefore, the goal of many experiments is to reduce the initial states to a small subset, and to measure the energy disposal in the products with the greatest accuracy. This was first achieved by controlling the kinetic energy of the reactants in crossed beam experiments. Later, a certain control of the collision geometry was obtained by orienting the molecules or the atomic orbitals in crossed beam experiments or by using prealigned systems in a van der Waals complex: this subject is discussed in Buelow et al. (1986).

scholarly journals Quantifying Climate Forcings and Feedbacks over the Last Millennium in the CMIP5–PMIP3 Models*

2016 ◽  
Vol 29 (3) ◽  
pp. 1161-1178 ◽  
Author(s):  
A. R. Atwood ◽  
E. Wu ◽  
D. M. W. Frierson ◽  
D. S. Battisti ◽  
J. P. Sachs
Keyword(s):  
Energy Budget ◽  
Climate Model ◽  
Ice Age ◽  
Lapse Rate ◽  
Last Millennium ◽  
Climate Feedbacks ◽  
Global Energy ◽  
Radiative Forcings ◽  
Global Cooling ◽  
Global Energy Budget

Abstract The role of radiative forcings and climate feedbacks on global cooling over the last millennium is quantified in the CMIP5–PMIP3 transient climate model simulations. Changes in the global energy budget over the last millennium are decomposed into contributions from radiative forcings and climate feedbacks through the use of the approximate partial radiative perturbation method and radiative kernels. Global cooling occurs circa 1200–1850 CE in the multimodel ensemble mean with pronounced minima corresponding with volcanically active periods that are outside the range of natural variability. Analysis of the global energy budget during the last millennium indicates that Little Ice Age (LIA; 1600–1850 CE) cooling is largely driven by volcanic forcing (comprising an average of 65% of the total forcing among models), while contributions due to changes in land use (13%), greenhouse gas concentrations (12%), and insolation (10%) are substantially lower. The combination of these forcings directly contributes to 47% of the global cooling during the LIA, while the remainder of the cooling arises from the sum of the climate feedbacks. The dominant positive feedback is the water vapor feedback, which contributes 29% of the global cooling. Additional positive feedbacks include the surface albedo feedback (which contributes 7% of the global cooling and arises owing to high-latitude sea ice expansion and increased snow cover) and the lapse rate feedback (which contributes an additional 7% of the global cooling and arises owing to greater cooling near the surface than aloft in the middle and high latitudes).

scholarly journals Understanding mixing efficiency in the oceans: do the nonlinearities of the equation of state for seawater matter?

Ocean Science ◽  
2009 ◽  
Vol 5 (3) ◽  
pp. 271-283 ◽  
Author(s):  
R. Tailleux
Keyword(s):  
Equation Of State ◽  
Potential Energy ◽  
Energy Conversion ◽  
Internal Energy ◽  
Molecular Diffusion ◽  
Rate Of Change ◽  
Gravitational Potential Energy ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Boussinesq Fluid

Abstract. There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

scholarly journals On the Consideration of Diffusive Fluxes Within High-Pressure Injections

2020 ◽  
pp. 195-208
Author(s):  
Fabian Föll ◽  
Valerie Gerber ◽  
Claus-Dieter Munz ◽  
Berhand Weigand ◽  
Grazia Lamanna
Keyword(s):  
Experimental Data ◽  
High Pressure ◽  
Significant Influence ◽  
Speed Of Sound ◽  
Mixing Model ◽  
Mixing Models ◽  
Relative Importance ◽  
Submerged Jets ◽  
Diffusive Fluxes ◽  
Sound Data

Abstract Mixing characteristics of supercritical injection studies were analyzed with regard to the necessity to include diffusive fluxes. Therefore, speed of sound data from mixing jets were investigated using an adiabatic mixing model and compared to an analytic solution. In this work, we show that the generalized application of the adiabatic mixing model may become inappropriate for subsonic submerged jets at high-pressure conditions. Two cases are discussed where thermal and concentration driven fluxes are seen to have significant influence. To which extent the adiabatic mixing model is valid depends on the relative importance of local diffusive fluxes, namely Fourier, Fick and Dufour diffusion. This is inter alia influenced by different time and length scales. The experimental data from a high-pressure n-hexane/nitrogen jet injection were investigated numerically. Finally, based on recent numerical findings, the plausibility of different thermodynamic mixing models for binary mixtures under high pressure conditions is analyzed.

scholarly journals Understanding mixing efficiency in the oceans: do the nonlinearities of the equation of state for seawater matter?

2009 ◽  
Vol 6 (1) ◽  
pp. 371-387
Author(s):  
R. Tailleux
Keyword(s):  
Equation Of State ◽  
Potential Energy ◽  
Linear Equation ◽  
Internal Energy ◽  
Molecular Diffusion ◽  
Rate Of Change ◽  
Gravitational Potential Energy ◽  
Mixing Efficiency ◽  
Nonlinear Character ◽  
Boussinesq Fluid

Abstract. There exist two central measures of turbulent diffusive mixing in turbulent stratified fluids, which are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the rate of change Wr,mixing of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as representing the same kind of energy conversion, i.e., the irreversible conversion of APE into GPEr, owing to the well known result that D(APE)≈Wr,mixing in a Boussinesq fluid with a linear equation of state. Here, this idea is challenged by showing that while D(APE) remains largely unaffected by a nonlinear equation of state, Wr,mixing is in contrast strongly affected by the latter. This result is rationalized by using the recent results of Tailleux (2008), which argues that D(APE) represents the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, whereas Wr,mixing represents the conversion between a different subcomponent of internal energy – called the "exergy" IEexergy – and GPEr. It follows that the concept of mixing efficiency, which represents the fraction of the stirring mechanical energy ultimately dissipated by molecular diffusion is related to D(APE), not Wr,mixing, which ensures that it should be largely unaffected by the nonlinear character of the equation of state, and therefore correctly described in the context of a Boussinesq fluid with a linear equation of state. The variations of GPEr, on the other hand, are sensitive to the linear or nonlinear character of the equation of state.

scholarly journals The Effect of Vertical Baroclinicity Concentration on Atmospheric Macroturbulence Scaling Relations

2017 ◽  
Vol 74 (5) ◽  
pp. 1651-1667 ◽  
Author(s):  
Janni Yuval ◽  
Yohai Kaspi
Keyword(s):  
Relaxation Time ◽  
Temperature Gradient ◽  
Potential Energy ◽  
Vertical Structure ◽  
Temperature Gradients ◽  
Lapse Rate ◽  
Meridional Temperature Gradient ◽  
Available Potential Energy ◽  
The Mean ◽  
Mean State

Abstract Motivated by the expectation that under global warming upper-level meridional temperature gradients will increase while lower-level temperature gradients will decrease, the relations between the vertical structure of baroclinicity and eddy fields are investigated. The sensitivity of eddies and the relation between the mean available potential energy and eddy quantities are studied for cases where the vertical structure of the lapse rate and meridional temperature gradient are modified. To investigate this systematically, an idealized general circulation model with a Newtonian cooling scheme that has a very short relaxation time for the mean state and a long relaxation time for eddies is used. This scheme allows for any chosen zonally mean state to be obtained with good precision. The results indicate that for similar change in the lapse rate or meridional temperature gradient, eddies are more sensitive to changes in baroclinicity where it is already large. Furthermore, when the vertical structure of the lapse rate or the meridional temperature gradient is modified, there is no universal linear relation between the mean available potential energy and eddy quantities.

scholarly journals Nonlinear Atmospheric Adjustment to Thermal Forcing

2005 ◽  
Vol 62 (12) ◽  
pp. 4253-4272 ◽  
Author(s):  
Paul F. Fanelli ◽  
Peter R. Bannon
Keyword(s):  
Steady State ◽  
Potential Energy ◽  
Wave Packet ◽  
Potential Vorticity ◽  
Lamb Wave ◽  
Static Stability ◽  
Lapse Rate ◽  
Thermal Forcing ◽  
The Waves ◽  
Buoyancy Waves

Abstract A nonlinear, numerical model of a compressible atmosphere is used to simulate the hydrostatic and geostrophic adjustment to a localized prescribed heating applied over five minutes with a size characteristic of an isolated, deep, cumulus cloud. This thermal forcing generates both buoyancy waves and a horizontally propagating Lamb wave packet as well as a steady state rich in potential vorticity. The adjustments in three model atmospheres (an isothermal, a constant lapse rate, and one with a stratosphere) are studied. The Lamb wave packet and the two lowest-order buoyancy waves are relatively unaffected by nonlinearities but the higher-order modes and the steady state are. The heating generates a vertically stacked dipole of potential vorticity with a cyclonic perturbation below an anticyclonic perturbation. In contrast to the linear results, the nonlinear dipole is severely distorted by vertical and horizontal advections. In addition, the Lamb wave packet contains some weak positive perturbation potential vorticity. The energetics is examined using traditional and Eulerian available energetics. Traditional energetics consists of kinetic, internal, and potential energies. It is shown that the Lamb wave packet contains more total traditional energy than that input to the atmosphere by the heating. The traditional energy in the packet resides primarily in the form of internal energy and only secondarily in the form of potential energy. The passage of the Lamb wave packet produces an atmosphere that, overall, is cooler, less dense, and with less total traditional energy than the initial atmosphere. Eulerian available energetics consists of kinetic, available potential, and available elastic energies. The heating generates both available elastic and potential energy that is then converted into kinetic energy. Most of the available elastic energy projects onto the Lamb packet, while almost all of the available potential energy is associated with the buoyancy waves and the steady state. The effects of varying the spatial and temporal scale of the heating, while keeping the net heating the same, are examined. As the duration of the heating decreases, the amount of energy projected onto the waves increases. Increasing the size of the heating decreases the amount of energy projected onto the waves. The adjustment is kinetically more vigorous in the nonisothermal atmospheres because of the reduction in the base-state static stability. The presence of a stratosphere produces large anomalies at and above the tropopause that are linked to the vertical motions of the buoyancy wave field.

scholarly journals Static Mantle Density Distribution 1 Equation

2019 ◽  
pp. 1-8 ◽  
Author(s):  
Tian Quan Yun
Keyword(s):  
Potential Energy ◽  
Density Distribution ◽  
Centrifugal Force ◽  
Seismic Waves ◽  
Vertical Direction ◽  
Gravitational Acceleration ◽  
Minimum Potential Energy ◽  
Fredholm Type ◽  
Minimum Potential ◽  
Two Parameters

The study of mantle distribution does relate to the reflecting of seismic waves, and has important meaning. Using Archimedes Principle of Sink or Buoyancy (APSB), Newton’s gravitation, buoyancy, lateral buoyancy, centrifugal force and the Principle of Minimum Potential Energy (PMPE), we derive equation of static mantle density distribution. It is a set of double-integral equations of Volterra/Fredholm type.  Some new results are: (1) The mantle is divorced into sink zone, neural zone and buoyed zone. The sink zone is located in a region with boundaries of a inclined line, with angle α1=35°15’ apex at  0(0,0,0) revolving around the z-axis, inside the crust involving the equator. The buoyed zone is located in the remainder part, inside the crust involving poles. The neural zone is the boundary between the buoyed and sink zones. The shape of core (in sink zone) is not a sphere. (2) The Potential energy inside the Earth is calculated by Newton’s gravity, buoyancy, centrifugal force and lateral buoyancy. (3) The gravitational acceleration above/on the crust is tested by formula with two parameters reflecting gravity and centrifugal force, and the phenomenon of “heavier substance sinks down in vertical direction due to attraction force, and moves towards to edges in horizontal direction due to centrifugal force” is tested by a cup of stirring coffee.

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