ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Physics of Lakes Volume 1: Foundation of the Mathematical and Physical Background

:	Kolumban Hutter, Wang Yongqi, Irina P. Chubarenko
:	Physics of Lakes Volume 1: Foundation of the Mathematical and Physical Background
:	Springer-Verlag
:	9783642151781
:	1
:	CHF 132.50
:

:	Geowissenschaften
:	English

:	434
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This first volume in the treatise on thePhysics of Lakes deals with the formulation of the mathematical and physical background. A large number of lakes on Earth are described, presenting their morphology as well as the causes of their response to the driving environment. Because the physics of lakes cannot be described without the language used in mathematics, these subjects are introduced first by using the simplest approach and with utmost care, assuming only a limited college knowledge of classical Newtonian physics, and continues with increasing complexity and elegance, starting with the fundamental equations of Lake Hydrodynamics in the form of 'primitive equations' and leading to a detailed treatment of angular momentum and vorticity. Following the presentation of these fundamentals turbulence modeling is introduced with Reynolds, Favre and other non-ergodic filters. The derivation of averaged field equations is presented with different closure schemes, including the k-ε model for a Boussinesq fluid and early anisotropic closure schemes. This is followed by expositions of surface gravity waves without rotation and an analysis of the role played by the distribution of mass within water bodies on the Earth, leading to a study of internal waves. The vertical structure of wind-induced currents in homogeneous and stratified waters and the Ekman theory and some of its extensions close this first volume of Physics of Lakes. The last chapter collects formulas for the phenomenological coefficients of water.

	Preface to the Book Series	7
	VOLUME 1: Physics of Lakes – Formulation of the Mathematical and Physical Background	8
	VOLUME 2: Physics of Lakes – Lakes as Oscillators	8
	VOLUME 3: Physics of Lakes – Methods of Understanding Lakes as Components of the Geophysical Environment	9
	Vorwort zur Buchreihe	10
	BAND 1: Physik der Seen – Formulierung des mathematischen und physikalischen Hintergrundes	11
	BAND 2: Physik der Seen – Seen als Oszillatoren	12
	BAND 3: Physik der Seen – Methoden, die Seen als Komponenten des geophysikalischen Umfeldes verstehen	12
	.pe..c.o..e . cep..	14
	Acknowledgements	21
	References	24
	Books, Reports	24
	Diploma (M. Sc.) Theses	24
	Doctoral Dissertations	25
	Habilitation Theses	26
	Preface to Volume I	27
	Acknowledgements for Copyright Permission	31
	Contents	33
	Notations	37
	Roman Symbols	37
	Greek Symbols	42
	Miscellaneous Symbols	44
	1 Introduction	46
	1.1 Motivation	46
	1.2 Lakes on Earth	55
	1.3 Lakes Characterised by Their Response to the Driving Environment	59
	1.3.1 Seasonal Characteristics	59
	1.3.2 Characteristics by Mixing	60
	1.3.3 Boundary-Related Processes	63
	1.3.4 Characterisation by Typical Scales	65
	References	67
	2 Mathematical Prerequisites	69
	2.1 Scalars and Vectors	70
	2.2 Tensors	82
	2.3 Fields and Their Differentiation	85
	2.4 Gradient, Divergence and Rotation of Vector and Tensor Fields	94
	2.5 Integral Theorems of Vector Analysis	104
	2.5.1 Gauss Theorems	104
	2.5.2 Stokes Theorems	106
	References	109
	3 A Brief Review of the Basic Thermomechanical Laws of Classical Physics	111
	3.1 Underlying Fundamentals -- General Balance Laws	111
	3.2 Physical Balance Laws	117
	3.2.1 Balance of Mass	117
	3.2.2 Balance of Linear Momentum	118
	3.2.3 Balance of Moment of Momentum	120
	3.2.4 Balance of Energy	121
	3.2.5 Second Law of Thermodynamics	123
	References	126
	4 Fundamental Equations of Lake Hydrodynamics	127
	4.1 Kinematics	128
	4.2 Balance of Mass	144
	4.3 Balances of Momentum and Moment of Momentum, Concept of Stress, Hydrostatics	154
	4.3.1 Stress Tensor	157
	4.3.2 Local Balance Law of Momentum or Newton's Second Law	162
	4.3.3 Material Behaviour	167
	4.3.4 Hydrostatics	172
	4.4 Balance of Energy: First Law of Thermodynamics	180
	4.5 Diffusion of Suspended Substances	185
	4.6 Summary of Equations	190
	4.7 A First Look at the Boussinesq and Shallow-Water Equations	194
	References	199
	5 Conservation of Angular Momentum--Vorticity	200
	5.1 Circulation	200
	5.2 Simple Vorticity Theorems	210
	5.3 Helmholtz Vorticity Theorem	213
	5.4 Potential Vorticity Theorem	220
	References	227
	6 Turbulence Modelling	228
	6.1 A Primer on Turbulent Motions	228
	6.1.1 Averages and Fluctuations	228
	6.1.2 Filters	230
	6.1.3 Isotropic Turbulence	233
	6.1.4 Reynolds Versus Favre Averages	235
	6.2 Balance Equations for the Averaged Fields	237
	6.2.1 Motivation	237
	6.2.2 Averaging Procedure	238
	6.2.3 Averaged Density Field	238
	6.2.3 Averaged Density Field	238
	240	238
	6.2.4 Dissipation Rate Density	238
	6.2.4 Dissipation Rate Density	238
	241	238
	6.2.5 Reynolds Stress Hypothesis	241
	6.2.6 One- and Two-Equation Models	244
	6.3 k–e Model for Density-Preserving and Boussinesq Fluids	246
	6.3.1 The Balance Equations	246
	6.3.2 Closure Relations	247
	6.3.3 Summary of (k–e)-Equations	249
	6.3.4 Boundary Conditions	250
	6.4 Final Remarks	253
	6.4.1 Higher Order RANS Models	253
	6.4.2 Large Eddy Simulation and Direct Numerical Simulation	254
	6.4.3 Early Anisotropic Closure Schemes	255
	References	262
	7 Introduction to Linear Waves	264