LEADER 01099cam0-22003251i-450 001 990000036690403321 005 20201211171803.0 035 $a000003669 035 $aFED01000003669 035 $a(Aleph)000003669FED01 035 $a000003669 100 $a20011111d1880----km-y0itay50------ba 101 0 $aita 102 $aIT 105 $aa-------001yy 200 1 $aSoluzioni e dimostrazioni dei problemi e teoremi dettati dai professori Enrico Betti e Francesco Brioschi come eserciziagli elementi d'Euclide$fAngelo Adriani 205 $a2. ed. riveduta e corretta. 210 $aNapoli$cB. Pellerano$d1880 215 $aXVI, 219 p.$cill.$d20 cm 610 0 $aGeometria euclidea 676 $a516.2 700 1$aAdriani,$bAngelo$0331686 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990000036690403321 952 $a13 AR 16 A 15$b23$fFINBC 959 $aFINBC 996 $aSoluzioni e dimostrazioni dei problemi e teoremi dettati dai professori Enrico Betti e Francesco Brioschi come eserciziagli elementi d'Euclide$9106173 997 $aUNINA DB $aING01 LEADER 07521nam 22005172 450 001 9910585954703321 005 20190502115337.0 010 $a1-108-67051-2 010 $a1-108-64008-7 035 $a(CKB)4970000000101560 035 $a(UkCbUP)CR9781108640084 035 $a(MiAaPQ)EBC5879497 035 $a(Au-PeEL)EBL5879497 035 $a(OCoLC)1101102230 035 $a(EXLCZ)994970000000101560 100 $a20171103d2019|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInstability in geophysical flows /$fWilliam D. Smyth, Jeffrey R. Carpenter$b[electronic resource] 205 $a1st ed. 210 1$aCambridge :$cCambridge University Press,$d2019. 215 $a1 online resource (xi, 327 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 19 Apr 2019). 311 $a1-108-70301-1 327 $aCover -- Half-title page -- Title page -- Copyright page -- Contents -- Preface -- Acknowledgments -- Part I Normal Mode Instabilities -- 1 Preliminaries -- 1.1 What Is Instability? -- 1.2 Goals -- 1.3 Tools -- 1.4 Numerical Solution of a Boundary Value Problem -- 1.5 The Equations of Motion -- 1.6 Further Reading -- 1.7 Appendix: A Closer Look at Perturbation Theory -- 2 Convective Instability -- 2.1 The Perturbation Equations -- 2.2 Simple Case: Inviscid, Nondiffusive, Unbounded Fluid -- 2.3 Viscous and Diffusive Effects -- 2.4 Boundary Effects: the Rayleigh-Benard Problem -- 2.5 Nonlinear Effects -- 2.6 Summary -- 2.7 Appendix: Waves and Convection in a Compressible Fluid -- 3 Instabilities of a Parallel Shear Flow -- 3.1 The Perturbation Equations -- 3.2 Rayleigh's Equation -- 3.3 Analytical Example: the Piecewise-Linear Shear Layer -- 3.4 Solution Types for Rayleigh's Equation -- 3.5 Numerical Solution of Rayleigh's Equation -- 3.6 Shear Scaling -- 3.7 Oblique Modes and Squire Transformations -- 3.8 Rules of Thumb for a General Shear Instability -- 3.9 Numerical Examples -- 3.10 Perturbation Energetics -- 3.11 Necessary Conditions for Instability -- 3.12 The Wave Resonance Mechanism of Shear Instability -- 3.13 Quantitative Analysis of Wave Resonance -- 3.14 Summary -- 3.15 Appendix: Classical Proof of the Rayleigh and Fjørtoft Theorems -- 3.16 Further Reading -- 4 Parallel Shear Flow: the Effects of Stratification -- 4.1 The Richardson Number -- 4.2 Equilibria and Perturbations -- 4.3 Oblique Modes -- 4.4 The Taylor-Goldstein Equation -- 4.5 Application to Internal Wave Phenomena -- 4.6 Analytical Examples of Instability in Stratified Shear Flows -- 4.7 The Miles-Howard Theorem -- 4.8 Howard's Semicircle Theorem -- 4.9 Energetics -- 4.10 Summary -- 4.11 Further Reading -- 4.12 Appendix: Veering Flows -- 4.13 Appendix: Spatial Growth. 327 $a5 Parallel Shear Flow: the Effects of Viscosity -- 5.1 Conditions for Equilibrium -- 5.2 Conditions for Quasi-Equilibrium: the Frozen Flow Approximation -- 5.3 The Orr-Sommerfeld Equation -- 5.4 Boundary Conditions for Viscous Fluid -- 5.5 Numerical Solution of the Orr-Sommerfeld Equation -- 5.6 Oblique Modes -- 5.7 Shear Scaling and the Reynolds Number -- 5.8 Numerical Examples -- 5.9 Perturbation Energetics in Viscous Flow -- 5.10 Summary -- 6 Synthesis: Viscous, Diffusive, Inhomogeneous, Parallel Shear Flow -- 6.1 Expanding the Basic Equations -- 6.2 Numerical Solution -- 6.3 2D and Oblique Modes: Squire Transformations -- 6.4 Shear and Diffusion Scalings -- 6.5 Application: Instabilities of a Stably Stratified Shear Layer -- 6.6 Application: Analysis of Observational Data -- 6.7 Summary -- 6.8 Further Reading -- 7 Nonparallel Flow: Instabilities of a Cylindrical Vortex -- 7.1 Cyclostrophic Equilibrium -- 7.2 The Perturbation Equations -- 7.3 Barotropic Modes (m = 0) -- 7.4 Axisymmetric Modes (l = 0) -- 7.5 Analytical Example: the Rankine Vortex -- 7.6 Numerical Example: a Continuous Vortex -- 7.7 Wave Interactions in Barotropic Vortices -- 7.8 Mechanisms of Centrifugal and Convective Instabilities -- 7.9 Swirling Flows -- 7.10 Summary -- 7.11 Further Reading -- 8 Instability in a Rotating Environment -- 8.1 Frontal Zones -- 8.2 Geostrophic Equilibrium and the Thermal Wind Balance -- 8.3 The Perturbation Equations -- 8.4 Energetics -- 8.5 The Vertical Vorticity Equation -- 8.6 Analytical Solution #1: Inertial and Symmetric Instabilities -- 8.7 Analytical Solution #2: Baroclinic Instability -- 8.8 Numerical Solution Method -- 8.9 Instability in the Ageostrophic Regime -- 8.10 Summary -- 8.11 Further Reading -- 9 Convective Instability in Complex Fluids -- 9.1 Conditional Instability in a Moist Atmosphere or a Freezing Ocean. 327 $a9.2 Double Diffusive Instabilities -- 9.3 Bioconvection -- 9.4 CO[sub(2)] Sequestration -- 10 Summary -- 10.1 Equilibrium States -- 10.2 Instabilities -- Part II The View Ahead -- 11 Beyond Normal Modes -- 11.1 Instability as an Initial Value Problem -- 11.2 Transient Growth in Simple Linear Systems -- 11.3 Computing the Optimal Initial Condition -- 11.4 Optimizing Growth at t = 0[sup(+)] -- 11.5 Growth at Short and Long Times: a Simple Example -- 11.6 Example: The Piecewise Shear Layer -- 11.7 Mechanics of Transient Growth in a Shear Layer -- 11.8 Generalizing the Inner Product -- 11.9 Summary -- 11.10 Appendix: Singular Value Decomposition -- 11.11 Further Reading -- 12 Instability and Turbulence -- 12.1 Secondary Instabilities and the Transition to Turbulence -- 12.2 Turbulence-Driven Instabilities -- 12.3 Cyclic Instability -- 12.4 Further Reading -- 13 Refining the Numerical Methods -- 13.1 Higher-Order Finite Differences -- 13.2 Finite Differences on an Adaptive Grid -- 13.3 Galerkin Methods -- 13.4 The Shooting Method -- 13.5 Generalizations -- 13.6 Further Reading -- Appendix A Homework Exercises -- Appendix B Projects -- References -- Index. 330 $aInstabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environmental science. Exercise solutions and MATLAB® examples are provided online. Also available as Open Access on Cambridge Core. 606 $aGeophysics 606 $aGeodynamics 606 $aMarine geophysics 615 0$aGeophysics. 615 0$aGeodynamics. 615 0$aMarine geophysics. 676 $a551.46/8 700 $aSmyth$b William D.$01253032 702 $aCarpenter$b Jeffrey R.$f1979- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910585954703321 996 $aInstability in geophysical flows$92905122 997 $aUNINA