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Internal wave dynamics in lakes (and oceans) is an important physical component of geophysical fluid mechanics of ‘quiescent’ water bodies of the Globe. The formation of internal waves requires seasonal stratification of the water bodies and generation by (primarily) wind forces. Because they propagate in basins of variable depth, a generated wave field often experiences transformation from large basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson number sufficiently small (< ¼), the light epilimnion water mixes with the water of the hypolimnion, giving rise to vertical diffusion of substances into lower depths. This meromixis is chiefly responsible for the ventilation of the deeper waters and the homogenization of the water through the lake depth. These processes are mainly formed as a result of the physical conditions, but they play biologically an important role in the trophicational state of the lake.

Internal waves. --- Lakes. --- Internal waves --- Lakes --- Geography --- Physics --- Earth & Environmental Sciences --- Physical Sciences & Mathematics --- Physical Geography --- Cosmic Physics --- Marine Science --- Lochs --- Boundary waves (Oceanography) --- Waves, Internal --- Earth sciences. --- Geophysics. --- Mathematical physics. --- Mechanics. --- Marine sciences. --- Freshwater. --- Earth Sciences. --- Geophysics/Geodesy. --- Marine & Freshwater Sciences. --- Mathematical Physics. --- Bodies of water --- Ocean waves --- Physical geography. --- Marine Sciences. --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Ocean sciences --- Aquatic sciences --- Physical mathematics --- Fresh waters --- Freshwater --- Freshwaters --- Inland water --- Inland waters --- Water --- Geological physics --- Terrestrial physics --- Earth sciences --- Mathematics

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Classical mechanics. Field theory --- Geophysics --- Hunting. Fishery. Aquaculture --- Physical geography --- aquacultuur --- wetenschappen --- fysische geografie --- mechanica --- geofysica

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Mixture concepts are nowadays used in a great number of subjects of the biological, chemical, engineering, natural and physical sciences (to name these alphabetically) and the theory of mixtures has attained in all these disciplines a high level of expertise and specialisation. The digression in their development has on occasion led to differences in the denotation of special formulations as ‘multi-phase systems’ or ‘non-classical mixtures’, ‘structured mixtures’, etc. , and their representatives or defenders often emphasise the differences of these rather than their common properties. Thismonographisanattempttoviewtheoreticalformulationsofprocesses which take place as interactions among various substances that are spatially intermixed and can be viewed to continuously ?llthe space which they occupy as mixtures. Moreover, we shall assume that the processes can be regarded to be characterised by variables which obey a certain degree of continuity in their evolution, so that the relevant processes can be described mathematically by balance laws, in global or local form, eventually leading to differential and/or integral equations, to which the usual techniques of theoretical and numerical analysis can be applied. Mixtures are generally called non-classical, if, apart from the physical laws (e. g. balances of mass, momenta, energy and entropy), also further laws are postulated,whicharelessfundamental,butmaydescribesomefeaturesofthe micro-structure on the macroscopic level. In a mixture of fluids and solids – these are sometimes called particle laden systems–the fraction of the volume that is occupied by each constituent is a significant characterisation of the micro-structure that exerts some influence on the macro-level at which the equations governing the processes are formulated. For solid-fluid mixtures at high solids fraction where particle contact is essential, friction between the particles gives rise to internal stresses, which turn out to be best described by an internal symmetric tensor valued variable.

Thermodynamics. --- Thermodynamics --- Physics --- Physical Sciences & Mathematics --- Electricity & Magnetism --- Cosmic Physics --- Friction materials. --- Earth sciences. --- Geophysics. --- Continuum physics. --- Earth Sciences. --- Geophysics/Geodesy. --- Classical Continuum Physics. --- Earth Sciences, general. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Geological physics --- Terrestrial physics --- Earth sciences --- Geosciences --- Environmental sciences --- Physical sciences --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Heat --- Heat-engines --- Quantum theory --- Brakes --- Friction --- Materials --- Physical geography. --- Geography. --- Classical and Continuum Physics. --- Cosmography --- World history --- Geography

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This third volume describes continuous bodies treated as classical (Boltzmann) and spin (Cosserat) continua or fluid mixtures of such bodies. It discusses systems such as Boltzmann continua (with trivial angular momentum) and Cosserat continua (with nontrivial spin balance) and formulates the balance law and deformation measures for these including multiphase complexities. Thermodynamics is treated in the spirit of Müller–Liu: it is applied to Boltzmann-type fluids in three dimensions that interact with neighboring fluids on two-dimensional contact surfaces and/or one-dimensional contact lines. For all these situations it formulates the balance laws for mass, momenta, energy, and entropy. Further, it introduces constitutive modeling for 3-, 2-, 3-d body parts for general processes and materially objective variable sets and their reduction to equilibrium and non-equilibrium forms. Typical (reduced) fluid spin continua are liquid crystals. Prominent nematic examples of these include the Ericksen–Leslie–Parodi (ELP) formulation, in which material particles are equipped with material unit vectors (directors). Nematic liquid crystals with tensorial order parameters of rank 1 to n model substructure behavior better, and for both classes of these, the book analyzes the thermodynamic conditions of consistency. Granular solid–fluid mixtures are generally modeled by complementing the Boltzmann laws with a balance of fluctuation (kinetic) energy of the particles. The book closes by presenting a full Reynolds averaging procedure that accounts for higher correlation terms e.g. a k-epsilon formulation in classical turbulence. However, because the volume fraction is an additional variable, the theory also incorporates ‘k-epsilon equations’ for the volume fraction.

Fluid mechanics. --- Thermodynamics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Hydromechanics --- Continuum mechanics --- Physical geography. --- Crystallography. --- Geophysics/Geodesy. --- Soft and Granular Matter, Complex Fluids and Microfluidics. --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Geography --- Geophysics. --- Amorphous substances. --- Complex fluids. --- Geological physics --- Terrestrial physics --- Earth sciences --- Complex liquids --- Fluids, Complex --- Amorphous substances --- Liquids --- Soft condensed matter

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In this book fluid mechanics and thermodynamics (F&T) are approached as interwoven, not disjoint fields. The book starts by analyzing the creeping motion around spheres at rest: Stokes flows, the Oseen correction and the Lagerstrom-Kaplun expansion theories are presented, as is the homotopy analysis. 3D creeping flows and rapid granular avalanches are treated in the context of the shallow flow approximation, and it is demonstrated that uniqueness and stability deliver a natural transition to turbulence modeling at the zero, first order closure level. The difference-quotient turbulence model (DQTM) closure scheme reveals the importance of the turbulent closure schemes’ non-locality effects. Thermodynamics is presented in the form of the first and second laws, and irreversibility is expressed in terms of an entropy balance. Explicit expressions for constitutive postulates are in conformity with the dissipation inequality. Gas dynamics offer a first application of combined F&T. The book is rounded out by a chapter on dimensional analysis, similitude, and physical experiments.

Mathematics --- Mathematical physics --- Fluid mechanics --- Thermodynamics --- Geophysics --- Geology. Earth sciences --- thermodynamica --- wiskunde --- geografie --- geologie --- ingenieurswetenschappen --- fysica --- aarde (astronomie) --- geofysica --- vloeistoffen