Motion, laws atmospheric

For very dilute solutions, the motion of the ionic atmosphere in the direction of the coordinates can be represented by the movement of a sphere with a radius equal to the Debye length Lu = k 1 (see Eq. 1.3.15) through a medium of viscosity t] under the influence of an electric force ZieExy where Ex is the electric field strength and zf is the charge of the ion that the ionic atmosphere surrounds. Under these conditions, the velocity of the ionic atmosphere can be expressed in terms of the Stokes law (2.6.2) by the equation... 

How Torricelli s invention measures the pressure of the atmosphere is explained by Newton s second law of motion, which states ... 

This result may be interpreted as showing that the ionic atmosphere has a charge —z, opposite to that of the ion on which attention is focused. Furthermore, the atmosphere has an effective radius equal to u + 1 /k. The motion of the atmosphere is in the opposite direction to that of the ion whose velocity is given by Stokes law. 

To describe the theoretical dynamical and thermal behavior of the atmosphere, the fundamental equations of fluid mechanics must be employed. In this section these equations are presented in a relatively simple form. A more conceptual view will be presented in Section 3.6. The circulation of the Earth s atmosphere is governed by three basic principles Newton s laws of motion, the conservation of energy, and the conservation of mass. Newton s second law describes the response of a fluid to external forces. In a frame of reference which rotates with the Earth, the first fundamental equation, called the momentum equation, is given by ... 

Flowing fluids are ubiquitous in Nature, from large scale atmospheric winds and oceanic currents to the circulation of blood or flow around microorganisms swimming in a liquid media. Fluid motion is also important in industrial processing and affects the motion of vehicles (cars, aircrafts etc.). In this chapter we briefly review the basic concepts and fundamental laws describing the motion of fluids. More details can be found in fluid dynamics textbooks (see, e.g. Batchelor (1967), Lamb (1932), Landau and Lifschitz (1959), Tritton (1988)). 

The relative motion of particle pairs in three-dimensional homogeneous turbulence was first described by L.F. Richardson based on experimental data on atmospheric dispersion. Well before the theoretical results of Kolmogorov on turbulent flows he suggested that the average distance between pairs of particles grows according to a power law of the form (Richardson, 1926)... 

The sedimentation of particles—that is, their downward motion due to gravitational settling—follows Stokes s law. Turbulent diffusion represents an opposing force, and sedimentation equilibrium is established when both forces cancel. Assuming a constant production rate of particles at the earth surface for each size group and a balance of upward and downward fluxes in the atmosphere leads to the following equation ... 

If the density of the air parcel is lower than that of the air surrounding it, the parcel will be more buoyant and will rise. If the air has a lower density, the parcel will decelerate and buoyancy will oppose its motion. The air parcel has the same pressure as the surrounding atmosphere, so using the ideal-gas law (16.21) becomes... 

Hydrodynamic models of the atmosphere on a grid or spectral resolution that determine the surface pressure and the vertical distributions of velocity, temperature, density, and water vapor as functions of time from the mass conservation and hydrostatic laws, the first law of thermodynamics, Newton s second law of motion, the equation of state, and the conservation law for water vapor. Abbreviated as GCM. Atmospheric general circulation models are abbreviated AGCM, while oceanic general circulation models are abbreviated OGCM. geomorphology... 

The origin of the power law decay is still not clearly understood. Possible origins include (i) a contribution from the ion atmosphere due to the counter ions and (ii) correlated motion of the water molecules along the grooves. The first contribution could be related to the well-known Debye-Falkenhagen effect which arises from correlated ion motion. The second contribution can arise from correlated motion of water molecules between grooves. 

It turns out that turbulent diffusion can be described with Fick s laws of diffusion that were introduced in the previous section, except that the molecular diffusion coefficient is to be replaced by an eddy or turbulent diffusivity E. In contrast to molecular diffusivities, eddy dififusivities are dependent only on the phase motion and are thus identical for the transport of different chemicals and even for the transport of heat. What part of the movement of a turbulent fluid is considered to contribute to mean advective motion and what is random fluctuation (and therefore interpreted as turbulent diffusion) depends on the spatial and temporal scale of the system under investigation. This implies that eddy diffusion coefficients are scale dependent, increasing with system size. Eddy diffusivities in the ocean and atmosphere are typically anisotropic, having much large values in the horizontal than in the vertical dimension. One reason is that the horizontal extension of these spheres is much larger than their vertical extension, which is limited to approximately 10 km. The density stratification of large water bodies further limits turbulence in the vertical dimension, as does a temperature inversion in the atmosphere. Eddy diffusivities in water bodies and the atmosphere can be empirically determined with the help of tracer compounds. These are naturally occurring or deliberately released compounds with well-estabhshed sources and sinks. Their concentrations are easily measured so that their dispersion can be observed readily. 

In the rarefied intellectual atmosphere of London, Hooke began his independent career of many astouhdingly diversified achievements. He enunciated the relationship known as Hooke s law, which states that stretching in an elastic body, such as a spring, is proportional to the force applied. This law was later used to describe the motion of atomic nuclei in molecules. Hooke used a telescope to make several original astronomical observations and a microscope to describe snowflakes, cells (a word he first used), and microscopic fossils. Hooke speculated on using the barometer to predict weather, but he later doubted its efficacy, confounded no doubt by variables that weather forecasters still struggle with today. 

Atmospheric mesoscale models are based on a set of conservation equations for velocity, heat, density, water, and other trace atmospheric gases and aerosols. The equation of state used in these equations is the ideal law. The conservation-of-velocity equation is derived from Newton s second law of motion (F = ma) as applied to the rotating earth. The conservation-of-heat equation is derived from the first law of thermodynamics. The remaining conservation equations are written as a change in an atmospheric variable (e.g., water) in a Lagrangian framework where sources and sinks are identified. 

DYNAMIC METEOROLOGY is the study of the motion of the atmosphere and the physical laws that govern that motion. Dynamic meteorology produces theories for atmospheric motion by applying basic principles from thermodynamics and classical mechanics. These principles are expressed mathematically as a set of partial differential equations. The goals of dynamic meteorology are twofold to understand the various types of atmospheric motion and to provide a basis for quantitative prediction of atmospheric phenomena. 

The laws of mechanics were first formulated by Isaac Newton in the middle of the seventeenth century. His second law states that the total rate of change of momentum is equal to the net applied force and is in the same direction as that force. Forces are thus inherent to changes in motioa The net force appearing in Newton s second law consists of the vector sum of component forces due to all sources. This section considers each of those component forces important for atmospheric motion. 

The governing equations of atmospheric motion consist of (1) Newton s second law in a form appropriate for a rotating coordinate system, (2) the first law of thermodynamics, (3) the continuity equation, and (4) the ideal gas law. These equations are summarized here ... 

The equations of motion relate the dynamics of flow to the pressure and density fields. The equation of mass continuity determines the time rate of change in the density field in terms of kinematics of flow. We now need a relationship between the time rate of change of pressure and density this is given by the first law of thermodynamics. The atmosphere is considered as an ideal gas, so that internal energy is a function of temperature only, and not density. We can also assume for an ideal gas that the specific heat at constant volume C is constant. 

The system of equations of horizontal motion [Eqs. (9) and (10)], hydrostatic equilibrium [Eq. (16)], mass continuity [Eq. (12)], thermodynamics [Eq. (8)], and the ideal gas law [Eq. (7)] is called the hydrostatic prediction model, or primitive equations. The hydrostatic assumption modifies the basic atmospheric prediction system in such a way as to eliminate the vertical propagation of sound waves. 

Astronomical events such as eclipses can be predicted matty years in advance with great precision. The laws governing celestial motions are precisely known from the dynamics of discrete bodies moving tmder gravitational fields, whereas the models itsed for predicting the motions of the atmosphere and oceans are approximate arrd nonlinear, involving very complex forcings. 

Climate models are governed by the laws of physics, which produce climate system components affecting the atmosphere, cryosphere, oceans, and land. No climate model would exist without an understanding of Newtonian mechanics and the fundamental laws of thermodynamics. By the late eighteenth century, scientific understanding of these physical laws allowed for numerical calculations to define observable climate processes. By the early twentieth century, scientists understood atmospheric phenomena as the product of preceding phenomena defined by physical laws. If one has accurate observable data of the atmosphere at a particular time and understands the physical laws under which atmospheric phenomena take place, it is possible to predict the outcome of future atmospheric changes. Mathematical equations were subsequently developed to define atmospheric motions and simulate observable processes and features of climate system components. 

On the other hand, we may look at thermal feeling of our planetary ecosystems, which, in general, is influenced by positioning in interstellar space [9,191]. No planet is a closed system neither is it in contact with two or more thermal baths. Each planet is in contact with a hot radiator (sun 5800 K) and cold radiation sinks (outer space 2.75 K). Each planet therefore realizes a kind of a specific cosmological engine. Being a sphere is crucial because of its rotation and revolution modes with an inclined axis, which are responsible for the richness and complexity in the behavior induced by the solar influx. The atmospheric fluid motion adds the spice of chaos so that the thermodynamic events, which take place within a planet, are sustained by non-equilibrium flows, which must obey the fundamental laws of non-equilibrium thermodynamics. 

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