Tropical Cyclones

Observations and Basic Processes

1st Edition, Volume 4 - September 22, 2023
Imprint: Elsevier
Authors: Roger K. Smith, Michael T. Montgomery
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 1 3 4 4 9 - 4
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 1 3 4 5 0 - 0

Tropical cyclones are a major threat to life and property, even in the formative stages of their development. They include a number of different hazards that individually can ca… Read more

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Tropical cyclones are a major threat to life and property, even in the formative stages of their development. They include a number of different hazards that individually can cause significant impacts, such as extreme winds, storm surge, flooding, tornadoes, and lightning. Tropical Cyclones: Observations and Basic Processes provides a modern overview of the theory and observations of tropical cyclone structure and behavior.

The book begins by summarizing key observations of the structure, evolution, and formation of tropical cyclones. It goes on to develop a theoretical foundation for a basic understanding of tropical cyclone behavior during the storm’s life cycle. Horizontally two-dimensional dynamics of vortex motion and other non-axisymmetric features are considered first before tackling the axisymmetric balance dynamics involving the overturning circulation. Following a review of moist convective processes, later chapters focus mainly on a range of three-dimensional aspects of the tropical cyclone life cycle. Building from first principles, the book provides a state-of-the-art summary of the fundamentals of tropical cyclones aimed at advanced undergraduates, graduate students, tropical meteorologists, and researchers.

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Title of Book
Cover image
Title page
Table of Contents
Copyright
Dedication
Epigraph
Preface
Acknowledgments
Nomenclature
Chapter 1: Observations of tropical cyclones
1.1. Tropical-cyclone tracks
1.2. Structure
1.2.1. Formation and intensification of Hurricane Patricia
1.2.2. Flight level wind structure and temperature structure
1.2.3. Vertical cross sections in Hurricane Edouard (2015)
1.2.4. Low-level structure of Hurricanes Isabel (2003) and Earl (2010)
1.2.5. Thermodynamic structure of Hurricane Earl's eye and eyewall
1.2.6. Intensity, strength, and size
1.2.7. Asymmetries
1.2.8. Secondary eyewalls
1.3. Surface heat and moisture supply
1.4. Ocean interaction
1.5. Tropical cyclone genesis
1.5.1. Formation regions
1.5.2. Necessary conditions for formation
1.5.3. Highlights from field experiments
1.5.4. The formation of a tropical depression
1.5.5. The multi-scale nature of genesis in the real world
1.5.6. Practical outcomes
1.6. Synthesis
Chapter 2: Fluid dynamics and moist thermodynamics
2.1. The equations of motion
2.2. Buoyancy and perturbation pressure
2.3. Thermodynamics
2.3.1. Equation of state
2.3.2. Thermodynamic energy equation
2.3.3. Potential temperature and specific entropy
2.3.4. Static energy
2.4. Prognostic and diagnostic equations
2.5. Moist processes
2.5.1. Equation of state for moist air
2.5.2. Saturation and latent heat release
2.5.3. Pseudo-adiabatic ascent
2.5.4. Equivalent potential temperature, moist entropy, moist static energy
2.6. Viscosity, diffusion, friction, and turbulence
2.7. Methods of solution
2.8. Kinetic energy and total energy
2.9. Vorticity and the vorticity equation
2.10. Vorticity-streamfunction method
2.11. Circulation
2.11.1. Kelvin's theorem
2.11.2. Beyond barotropy
2.12. Potential vorticity
2.13. Balance dynamics
2.14. PV global constraints
2.15. PV flux form and impermeability theorem
2.16. Vorticity flux equation
2.17. Coordinate systems
2.18. Exercises
2.19. Appendix: the membrane analogy
Chapter 3: Tropical cyclone motion
3.1. The observations to be explained
3.2. The partitioning problem
3.3. Prototype problems
3.3.1. Symmetric vortex in a uniform flow
3.3.2. Vortex motion on a β-plane
3.3.3. The effects of an environmental flow
3.3.4. More general environmental flows
3.4. Observations of the β-gyres
3.5. Exercises
3.6. Appendices
3.6.1. Appendix 1: transformation of the momentum equation to an accelerating frame of reference
3.6.2. Appendix 2: derivation of Eq. (3.14)
3.6.3. Appendix 3: solution of Eq. (3.22)
Chapter 4: Vortex axisymmetrization, waves and wave-vortex interaction
4.1. Illustration of flow asymmetries
4.1.1. Examples of vortex axisymmetrization
4.2. Vortex merger and separation, Fujiwhara effect
4.3. The pseudo-mode
4.4. Vortex shear waves and vortex Rossby waves
4.4.1. Force balances in a circular vortex
4.4.2. Vortex waves and instabilities
4.4.3. Generalized Rayleigh and Fjortoft instability theorems
4.4.4. Solution to initial value problems
4.4.5. Case I: bounded Rankine vortex: V=Γ/r, Ω=Γ/r2, Γ = constant, a⩽r⩽b
4.4.6. More on vortex waves
4.4.7. Relevance to tropical cyclones
4.4.8. Case II: unbounded Rankine vortex
4.4.9. Case III: unbounded Rankine-like vortex with multiple discontinuities in ζ
4.5. Wave-vortex interaction
4.5.1. Effect of discrete VR wave only
4.5.2. Effect of exterior disturbance on outer flow
4.5.3. Effect of exterior disturbances on vmax
4.5.4. Effect of near-core disturbances on vmax
4.5.5. Model limitations applied to smooth vortices: quasi-modes
4.5.6. Resonant wave, vortex interaction
4.6. Synthesis
4.7. Enrichment topics
4.7.1. Vortex intensification by stochastic forcing with secondary circulation
4.7.2. Point vortex analog of wave, vortex model
4.7.3. VR wave pathway to secondary eyewall formation?
4.8. Exercises
Chapter 5: Axisymmetric vortex theory fundamentals
5.1. Equations of motion in rotating cylindrical polar coordinates
5.2. The primary circulation
5.3. Interpretation of the thermal wind equation
5.4. Generalized buoyancy
5.4.1. Exercises
5.5. The tropical cyclone eye
5.6. Spin up of the primary circulation
5.7. Stability
5.7.1. Barotropic vortices
5.7.2. Exercises
5.7.3. Baroclinic vortices
5.7.4. Exercises
5.8. Scale analysis
5.8.1. Continuity equation
5.8.2. Momentum equations
5.8.3. Thermodynamic equation
5.8.4. Exercise
5.9. The secondary circulation
5.9.1. Exercises
5.10. Solutions of the Eliassen equation
5.10.1. Boundary effects in the membrane analogy
5.10.2. Scale effects in the membrane analogy
5.10.3. Other anisotropic effects in the membrane analogy
5.10.4. Exercise
5.10.5. Point source solutions in an unbounded domain
5.10.6. Point source solutions in a partially bounded domain
5.11. Representation of the diabatic heating rate, θ˙
5.12. Buoyancy relative to a balanced vortex
5.12.1. Local buoyancy and system buoyancy
5.13. Enrichment topics
5.13.1. Toroidal vorticity equation
5.13.2. Eliassen equation and toroidal vorticity equation
5.13.3. Geopotential tendency equation
5.13.4. Deductions from the spin-up function
5.13.5. The linear approximation, the Eliassen equation and extension to include unbalanced forcing
Chapter 6: Frictional effects
6.1. Vortex spin down
6.2. Scale analysis of the equations with friction
6.2.1. w-momentum equation
6.2.2. u- and v-momentum equations
6.2.3. Boundary layer depth scale
6.2.4. Boundary layer equations
6.3. The Ekman layer
6.4. The linear approximation
6.4.1. Physical interpretation
6.4.2. Mathematical solution
6.4.3. Vertical structure of the solution
6.4.4. Observed wind structure
6.4.5. Radial-vertical structure
6.4.6. Interpretation, torque balance
6.4.7. Factors determining the inflow and vertical motion
6.4.8. Dependence on vortex size
6.4.9. Supergradient winds in the linear solution
6.4.10. Exercises
6.4.11. Limitations of linear theory
6.5. A nonlinear slab boundary layer model
6.5.1. The boundary layer equations
6.5.2. Representation of surface and top fluxes
6.5.3. The final equations
6.5.4. Starting conditions at large radius
6.5.5. Exercise
6.5.6. Slab boundary layer solutions
6.5.7. Physical interpretation
6.6. The boundary-layer spin up enhancement mechanism
6.7. Limitations of the two boundary layer models
6.7.1. Advantages of the slab model
6.7.2. Limitations of boundary-layer theory in general
6.7.3. Balanced boundary layer approximation
6.8. Importance of the tropical cyclone boundary layer
6.9. Appendices
6.9.1. Appendix 1: radial variation of ν, I2, a1, and a2 in the linear boundary layer solution
6.9.2. Appendix 2: what determines the vertical velocity in the linear boundary layer?
6.9.3. Appendix 3: the upper boundary condition
Chapter 7: Estimating boundary layer parameters
7.1. Boundary layer structure, supergradient winds
7.2. Subgrid-scale parameterizations
7.3. Vertical diffusivity in the boundary layer
7.4. Horizontal diffusivity in the boundary layer
7.5. Air-sea interaction, drag coefficient, enthalpy coefficient
Chapter 8: A prognostic balance theory for vortex evolution
8.1. Solutions for the evolution of a balanced vortex
8.1.1. Diabatic heating, no friction
8.1.2. Friction, no heating
8.1.3. Diabatic heating and friction
8.2. Interpretation: the classical spin up mechanism
8.2.1. Exercises
8.3. Rotational stiffness, latitude dependence and vortex size evolution
8.3.1. A laboratory experiment
8.3.2. Balance considerations
8.3.3. Idealized balance simulations
8.3.4. Effects of friction on vortex size growth
8.3.5. Vortex intensity and size metrics
8.3.6. Dependence of frictionally-driven inflow on latitude
8.3.7. Summary
8.4. Interplay between diabatic heating and friction
8.4.1. Flow structure at the initial time
8.4.2. Flow structure at later times
8.4.3. Summary: the issue of convective ventilation
8.4.4. Pathological nature of the balanced boundary layer
8.4.5. Utility and limitations of the prognostic balance model
8.5. Appendix
Chapter 9: Moist convection
9.1. Convective instability
9.2. Aerological diagrams
9.2.1. CAPE and CIN
9.2.2. Height-temperature-difference diagram
9.2.3. More on aerological diagrams
9.2.4. The use of θe for assessing convective instability
9.3. Types of penetrative convection
9.3.1. Shallow convection
9.3.2. Intermediate convection
9.3.3. Deep convection
9.3.4. Convective downdrafts
9.4. Understanding the effects of deep convection on the tropical circulation
9.5. Buoyancy in a finite horizontal domain
9.6. Quantification of effective buoyancy
9.7. Implications for CAPE
9.8. More on CAPE
9.9. Cloud structure in tropical cyclones
9.9.1. Ventilation by deep convection in tropical cyclones
9.10. Exercises
9.11. Appendices
9.11.1. Appendix 1: effective buoyancy per unit volume
9.11.2. Appendix 2: numerical solution of Eq. (9.15)
9.11.3. Appendix 3: forcing of p′ by Fd in Eq. (9.15) on the upper domain axis
Chapter 10: Tropical cyclone formation and intensification
10.1. The prototype problem for genesis and intensification
10.2. A simplified numerical model experiment
10.3. The numerical simulation
10.3.1. A summary of vortex evolution
10.3.2. Evolution of vorticity
10.4. Moist instability and θe
10.5. Azimuthal mean view of vortex evolution
10.6. Modified view of spin up
10.7. A system-averaged perspective
10.8. Predictability issues
10.9. Inclusion of ice processes
10.10. Vortex evolution with and without ice
10.11. Moist instability and θe
10.12. An azimuthal mean view of vortex evolution
10.13. Mid-level vortex development with ice microphysics
10.13.1. Increasing influence of the boundary layer
10.13.2. Synthesis
10.14. Boundary layer control
10.14.1. Boundary layer coupling in brief
10.14.2. A demonstration of boundary layer coupling
10.15. Towards a conceptual model for tropical cyclogenesis
Chapter 11: The rotating-convection paradigm
11.1. Flux form of the vorticity equation
11.2. Axisymmetric flow
11.3. Non-axisymmetric flow
11.4. Azimuthally-averaged tangential and radial wind tendency
11.4.1. Characterizing eddy processes
11.4.2. Attributes of the mean-eddy flow partitioning
11.4.3. Eddy effects of an isolated deep convective cloud
11.5. Applications to a numerical model simulation
11.5.1. Tangential velocity tendency analysis
11.5.2. Spin up at later times
11.5.3. Radial velocity tendency analysis
11.5.4. Summary of radial velocity analysis at 30 h
11.6. Other features of the numerical simulation
11.6.1. Upper level inflow jets
11.6.2. Centrifugal recoil effect
11.7. Summary of the rotating-convection paradigm
Chapter 12: Emanuel's intensification theories
12.1. The intensification theories
12.1.1. The Emanuel 1989 theory
12.1.2. The Emanuel 1995 theory
12.1.3. The later theories
12.1.4. Specifics of the E97 theory
12.2. The air-sea interaction intensification theory, WISHE
12.3. The E12 theory
12.3.1. Specifics of the E12 theory
12.4. A boundary layer explanation for spin up
12.5. Congruence of M and θe⁎ surfaces during spin up?
12.6. Appraisal of the Emanuel intensification theories
12.7. Relevance to hurricanes in a warmer world?
12.8. Appendix: derivation of ∂vm/∂τ in the E12 theory, Eq. (12.4)
Chapter 13: Emanuel's maximum intensity theory
13.1. The E86 steady-state model
13.1.1. Dissipative heating
13.1.2. High resolution tests of the E86 PI theory
13.2. Unbalanced effects
13.3. A revised theory
13.4. Three dimensional effects
13.5. Summary of Emanuel's steady-state PI theories
13.6. Appendix A: Derivation of an extended PI model, Eq. (13.7)
13.6.1. Formulation for the free troposphere
13.6.2. Boundary layer closure
13.7. Appendix B: Construction of E86 steady-state hurricane solution
13.7.1. Conceptual overview
13.7.2. Deductions from thermal wind balance and moist neutrality
13.7.3. Boundary layer constraints
13.7.4. Solution for ln⁡π in Region III
13.7.5. Solution for ln⁡π in Regions I + II
13.7.6. Solution for vgmax2 and ln⁡πs at r=rgm
13.7.7. The complete solution
13.7.8. The tropical cyclone as a Carnot-like heat engine
13.8. Exercises
Chapter 14: Global budgets and steady state considerations
14.1. The numerical simulation
14.2. Budget calculations
14.2.1. Water budget
14.2.2. Kinetic energy budget (Gill form)
14.2.3. Kinetic energy budget (Anthes form)
14.2.4. Kinetic energy budget calculations
14.2.5. Total energy budget
14.3. Role of surface enthalpy fluxes
14.3.1. Contributions to θe changes
14.3.2. Some observations
14.4. Absolute angular momentum budget
14.5. Exercises
14.6. Global steady-state requirements
Chapter 15: Tropical cyclone life cycle
15.1. Newtonian cooling
15.2. Life cycle metrics
15.3. Vortex asymmetries
15.3.1. Genesis and RI phases
15.3.2. First mature phase
15.3.3. Decay phase
15.4. Azimuthally-averaged view of vortex evolution
15.4.1. Mature phase
15.4.2. Temporary decay and reintensification phase
15.4.3. A new pathway to inner-core rainband formation
15.4.4. Decay phase
15.5. Interpretations of the life cycle
15.5.1. Important kinematical features
15.5.2. Boundary layer dynamics
15.5.3. Boundary layer coupling
15.5.4. Ventilation of the boundary layer inflow
15.5.5. Convection component of ventilation
15.6. Life cycle summary
Chapter 16: Applications of the rotating-convection paradigm
16.1. Minimal conceptual models for vortex intensification
16.1.1. A general prognostic balance model
16.1.2. Zero-order model
16.1.3. A minimal representation of friction
16.1.4. First-order model
16.1.5. Exercises
16.1.6. Beyond the minimal representation of friction
16.1.7. Cumulus parameterization in minimal models
16.1.8. Role of the WISHE feedback?
16.1.9. Important caveats
16.1.10. Synthesis
16.2. Comparison between three-dimensional and axisymmetric tropical cyclone dynamics
16.2.1. Synthesis
16.3. The effects of latitude on tropical cyclone intensification
16.3.1. The Smith et al. (2015a) simulations
16.3.2. Vortex evolution at different latitudes
16.3.3. Slab boundary layer solutions
16.3.4. Thermodynamic support for deep convection
16.3.5. Diabatically-forced overturning circulation
16.3.6. Quantifying the effects of rotational stiffness
16.3.7. Flow asymmetries
16.3.8. Summary of latitudinal dependence
16.4. The effects of sea surface temperature on intensification
16.4.1. Interpretation of the SST dependence
16.4.2. Summary of SST effects
16.5. The effects of initial vortex size on genesis and intensification
16.5.1. Numerical experiments on vortex size
16.5.2. Synthesis
16.6. Tropical cyclogenesis at and near the Equator
16.6.1. An idealized numerical study
16.6.2. Synthesis
16.7. Observational tests of the rotating-convection paradigm
16.8. Tropical lows over land
16.8.1. A tropical low case study
16.8.2. Synthesis
16.9. Polar lows, medicanes and tropical cyclones
16.10. The rotating-convection paradigm in the research of others
16.10.1. An idealized numerical study
16.10.2. Formation of a thermodynamic shield in a Category 5 hurricane, but not in a Category 3 hurricane
16.10.3. Invocation of WISHE-like positive feedback mechanism to explain the rapid intensification of Hurricane Michael (2018)
16.10.4. Synthesis
16.11. Vertical shear regimes
16.11.1. Synthesis
Chapter 17: Epilogue
17.1. Examples of recent events
17.1.1. Formation and intensification of Hurricane Fiona (2022)
17.1.2. Increasing size of Hurricane Fiona
17.1.3. Formation and intensification of Hurricane Ian (2022)
17.1.4. Increasing size of Hurricane Ian
17.2. Applications and future directions
References
Index

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health

Tropical Cyclones

Observations and Basic Processes

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Roger K. Smith

Michael T. Montgomery

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