Fundamental Laws_Ocean Dynamic
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Part I Fundamental Laws The fundaments of ocean physics are based on the concepts of hydrodynamics and thermodynamics. Molecular structures of the media are not considered explicitly (except in radiation processes which, however, are not treated in this book). Physical properties of small but finite volume elements are defined according to the continuum hypothesis, e. g. a mean velocity or a mean concentration of constituents are defined locally at each point of the fluid domain. Such mean values are well defined because a volume of only 1 μm 3 of sea water or air contains more than 10 10 molecules. The A fluid parcel (also called fluid particle) is a small volume element moving with the local velocity, in case of seawater this is the barycentric velocity of the pure water and the salt con- stituents. The fluid parcel conserves its mass but may exchange material by dif- fusive processes with the surrounding fluid (pure wa- ter in/out and salt out/in). The sketch shows the parcel with a vectorial flux J of a substance through a sur- face element dA with nor- mal n. Further explanations are given in Chapter 2. average separation between molecules is much smaller than any relevant scale L over which variations of variables are considered. In water is only about 10 8 cm, whereas the smallest scale in microstructure measurements in the ocean is typically a few millimeters. With very good accuracy. the corresponding state variables can thus be regarded as continuous fields in space and time. The equations, which describe the evolution of the state of the ocean, are the macroscopic conservation theorems for partial masses, momentum, and internal en- ergy, as used in conventional hydrodynamics and thermodynamics. These macro- scopic theorems can in principle be derived from a statistical theory in which the basic physical laws, governing the microscopic state of single molecules, are em- bedded (see textbooks on statistical mechanics as e. g. Huang, 1987). The molecular structure of the fluid also determines the values of important parameters appearing in these equations, such as molecular diffusivities for momentum and partial masses, in terms of the forces acting between molecules. In this part we follow instead a phenomenological derivation of hydrodynamics, based on the empirical knowledge that mass, momentum and energy of small (ma- terial) volume elements moving in the fluid are conserved. The thermodynamics is also formulated for such volume elements, assuming that the properties are locally in a thermodynamical equilibrium. Thermodynamic and molecular properties then have to be taken from empirical findings. The macroscopic theory is built in this La- grangian point of view, but the evolution equations are transformed to the Eulerian form of a field theory which is more useful in applications.
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Transcript of Fundamental Laws_Ocean Dynamic
Part IFundamental Laws
The fundaments of ocean physics are based on the concepts of hydrodynamics andthermodynamics. Molecular structures of the media are not considered explicitly(except in radiation processes which, however, are not treated in this book). Physicalproperties of small but finite volume elements are defined according to the continuumhypothesis, e. g. a mean velocity or a mean concentration of constituents are definedlocally at each point of the fluid domain. Such mean values are well defined becausea volume of only 1 µm3 of sea water or air contains more than 1010 molecules. The
A fluid parcel (also calledfluid particle) is a smallvolume element movingwith the local velocity, incase of seawater this is thebarycentric velocity of thepure water and the salt con-stituents. The fluid parcelconserves its mass but mayexchange material by dif-fusive processes with thesurrounding fluid (pure wa-ter in/out and salt out/in).The sketch shows the parcelwith a vectorial flux J ofa substance through a sur-face element dA with nor-mal n. Further explanationsare given in Chapter 2.
average separation � between molecules is much smaller than any relevant scale L
over which variations of variables are considered. In water � is only about 10�8 cm,whereas the smallest scale in microstructure measurements in the ocean is typicallya few millimeters. With very good accuracy. the corresponding state variables canthus be regarded as continuous fields in space and time.
The equations, which describe the evolution of the state of the ocean, are themacroscopic conservation theorems for partial masses, momentum, and internal en-ergy, as used in conventional hydrodynamics and thermodynamics. These macro-scopic theorems can in principle be derived from a statistical theory in which thebasic physical laws, governing the microscopic state of single molecules, are em-bedded (see textbooks on statistical mechanics as e. g. Huang, 1987). The molecularstructure of the fluid also determines the values of important parameters appearingin these equations, such as molecular diffusivities for momentum and partial masses,in terms of the forces acting between molecules.
In this part we follow instead a phenomenological derivation of hydrodynamics,based on the empirical knowledge that mass, momentum and energy of small (ma-terial) volume elements moving in the fluid are conserved. The thermodynamics isalso formulated for such volume elements, assuming that the properties are locallyin a thermodynamical equilibrium. Thermodynamic and molecular properties thenhave to be taken from empirical findings. The macroscopic theory is built in this La-grangian point of view, but the evolution equations are transformed to the Eulerianform of a field theory which is more useful in applications.
