Lecture 3. Design Wind Speed. Tokyo Polytechnic University The 21st Century Center of Excellence Program. Yukio Tamura

Size: px
Start display at page:

Download "Lecture 3. Design Wind Speed. Tokyo Polytechnic University The 21st Century Center of Excellence Program. Yukio Tamura"

Transcription

1 Lecture 3 Design Wind Speed Tokyo Polytechnic University The 21st Century Center of Excellence Program Yukio Tamura Wind Climates Temperature Gradient due to Differential Solar Heating Density Difference Pressure Gradient (Conservation of mass/momentum) - Global Circulations (Hadley, 1973) - Monsoons - Frontal Depressions - Tropical Cyclones (Hurricanes, Typhoons, Cyclones) - Thunderstorms (Down Bursts) - Tornadoes - Devils - Gravity Winds (Katabatic( Winds) - Lee Waves etc. 1

2 Tropical Cyclones (Hurricanes, Typhoons) 1000 hpa 1000 hpa km EYE OF HURRICANE Temporal Variation of Wind Speed (Hurricane Celia, 1970) Maximum Peak Gust 19:00 20:00 21:00 22:00 23:00 24:00 1:00 Cook,

3 Wind Speed Distribution in Tropical Cyclones Wind Speed r 1 / r 0 r m 100 Distance from Center r Wind Speed Distribution in Tropical Cyclones Moving Direction 10m/s 20m/s 30m/s 40m/s 50m/s Dangerous Semicircle 3

4 Temporal Variation of Wind Speed (Typhoon) 13: m/s SSE 240m 180m 120m Cumulonimbus Downbursts Down Draft Down Draft 60m 600m Stagnation Cone Gust Front 1200m 1800m 2400m 3000m 3600m 4km Intense Blowoff 4

5 Tornadoes Cumulonimbus Geostrophic Wind Geostrophic Wind Speed U G dp + ρ a U G f = 0 dn ρ a Low Pressure High Pressure Pressure Force U G Coriolis Force : Air Density f : Coriolis Parameter = 2Ω sinφ = sinφ (rad/s) Ω : Earth s s Rotational Speed φ : Latitude Isobars 5

6 Gradient Wind Gradient Wind Speed U g (without consideration of ground surface friction ) Centrifugal Force Low Pressure dp U 2 g + ρ a U g f + ρ a = 0 dn r r : Radius of Curvature Isobars Pressure Force U g Coriolis Force High Pressure Atmospheric Boundary Layer Gradient Height Z g U g Friction Free Wind A.B.L. < Z g / 10 d Outer Layer 200m Surface Layer (τ : constant) Interfacial Layer d : Zero-plane displacement Average building height 6

7 Gradient Wind (Z( >Z g ) Pressure Gradient Force Coriolis Force + Centrifugal Force Outer Layer ( Z( g /10 < Z < Z g ) - Momentum transfer from Gradient Wind - Momentum delivered to lower altitude due to Friction Effects (Reynolds Stress : Turbulent Transfer) Strong Wind Condition - Sufficient mixing of air - Thermally neutral condition ( θ/ Z 0, θ :Temperature) - Effects of ground roughness are predominant. - Shear force (Reynolds stress: τ = ρ a uw ) increases from zero at the gradient height Z g to a maximum at the zero-plane displacement. - Surface shear stress: τ 0 = ρ a uw max = ρ a u 2 cf. Boussinesq: Kinetic Eddy Viscosity * du u * : Friction velocity ρ a uw = ρ a ε : Kinetic Eddy Viscosity ε dz 7

8 Ekman Layer Geostrophic Balance With Friction Low Pressure Pressure Force U Isobars Friction Force Coriolis Force High Pressure Lower Altitude U U G Ekman Spiral Wind Speed Fluctuation U(t ) = U + u(t u ) Fluctuating Component u(t) Mean Wind Speed U 8

9 Power Spectrum of Wind Speed (van der Hoven for Brookhaven, 1957) Power Spectral Density fs U (f) (m/s) 2 4days 1day Macrometeorological peak 1hour 10min 1min 5s Spectral Gap Micrometeorological peak Frequency f (cycle/hour) Long Term and Short Term Fluctuations Averaging Time of Wind Speed T = 10min (Japan, ISO4354, etc.) 1hour Long Term Fluctuation T > 10min 1hour --- Variation of Mean Wind Speed (Design Wind Speed) --- Static Effects on Buildings Short Term Fluctuation T < 10min 1hour --- Turbulence or Gust --- Dynamic Effects on Buildings 9

10 Mean Wind Speed Structure Geographical Location Ground Roughness and Height Topographic Effects Direction Seasonal Variation Return Period etc. Wind Speed Profile U g U g U g 10

11 Wind Speed Profile (Theoretical Approach) Surface Layer u * Z d U = { ln( ) ) + A } k z 0 Law of Wall (Prandtl( Prandtl,, 1932) Near Gradient Height u * u U * g = { ln( ) B } k f z 0 Velocity Defect Law (Karman, 1930) z 0 : Roughness length, u * : Friction velocity k : Karman constant ( ( 0.4) f : Coriolis parameter, A, B : Empirical constants Wind Speed Profile in Codes Log Law u * Z d U = ln( ) k z 0 - Uniform roughness & Constant τ Power Law (fully empirical) Z d U = U r ( ) α Z r z 0 : Roughness length, u * : Friction velocity k : Karman constant ( ( 0.4) d : Zero-plane displacement (0 0.75H) U r : Wind speed at reference height Z r Z r : Reference height, α : Power-law index Deaves & Harris Model (log + polynomial) 11

12 Wind Speed Profile (Field Data) Terrain z 0 α sea, mudflats, snow covered flat land, etc. flat open countryside, fields with crops, fences and few trees, etc. (Meteorological Standard) dense woodland, domestic housing, suburban area city large city center m m 0.003m - 0.2m 0.2m -1m 1m -2m 2m - 4m Wind speed difference between two sites with different roughnesses Site A Site B 12

13 Wind Speed Profiles at Two Sites with Different Roughnesses N Seaside Urban 12k 1 Urban 2 m Urban 2 Seaside Urban 2 Seaside Tokyo Bay Wind Speed Profile (AIJ Rec.1993) Large City Center Seaside AIJ

14 Yearly Variation of Annual Maximum Wind Speed and Building Volume in Japan Return Period : R Annual V Maximum Wind Speed U U R Vr r 1 N Rr = lim t i N N i = 1 0 t t 1 t (year) t 2 t 3 t 4 t 5 Return Period R = Mean Time Between Failure (MTBF) 14

15 Wind Speed U R and Return Period R Wind Speed U R (m/s) Return Period R (years) Annual probability of exceedence of wind speed U R : Q(U 1 R ) = R Probability of non-exceedence (CDF) of wind speed U R : 1 P(U R ) = 1 R Tokyo R-year Recurrence Wind Speed U R Probability of exceedence of U R during Building s Life Time, e.g. T L = 50 years T 1 Q(U R : T L ) = 1 P(U R ) L = 1 (1 ) R T L R (years) Q(U R : 50) % % % % (T L = 50 years) 15

16 Extreme Value Analysis (Asymptotic Form: Cumulative Distribution Function) Fisher-Tippett Type I (Gumbel( Distribution) CDF: P(U) ) = exp[ exp{ a(u b)}] 1/a : dispersion, b : mode Fisher-Tippett Type II (Frechet( Distribution) c γ CDF: P(U) ) = exp{ ( ) } U ε - having lower limit : ε Fisher-Tippett Type III (Weibull( Distribution) U w γ CDF: P(U) ) = exp{ ( ) } v w - having upper limit : w Gumbel Distribution CDF: P(U R ) = exp[ exp{ a(u R b)}] 1/a : dispersion, b : mode Cumulative Distribution Function of R-year Recurrence Wind Speed U R 1 P(U R ) = 1 R R-year Recurrence Wind Speed Based on Gumbel Distribution 1 1 U R = ln{ ln ( 1 ) } + b a R Modified Jensen-Franck Method (Cook, 1982) (Individual Storms, Gumbel,, Threshold) 16

17 Basic Design Wind Speed in Japan (AIJ Rec.1993) 100-year Recurrence 10-min Mean Z =10m, α = 0.15 (Category II) (m/s) Okinawa: 50m/s 48 Topographic Effects Escarpments Cliffs Ridges Hills Valleys - Speed-up Ratio (Mean Wind Speed) - Turbulence Speed-up Ratio : AIJ Rec

18 Topographic Effects Fluctuating Wind Speed Structure Gust Factor / Peak Factor Power Spectrum Spatial- / Temporal- Correlation Taylor s s Hypothesis of Frozen Turbulence Turbulence Intensity Turbulence Scale 18

19 Wind Speed Components z w U Mean Wind Speed Mean Wind Direction v u y x Temporal Variation of Wind Speed U(t ) = U + u(t u ) U max = U + u max Wind Speed Fluctuating Component u(t) Mean Wind Speed U σ u σ u Time (min) Turbulence Intensity I u σ u I u =, σ 2 u = S u (f)df U 19

20 Gust Factor and Peak factor Gust Factor: G U U max U + u G max U = = U U Peak Factor: g U u max σ uumax g U = max σ u G U = 1 + = 1 + g U = 1 + g U I U U U Turbulence Intensity (AIJ Rec.1993) Height Z (m) Terrain Category I II III V IV I 0.5 u 20

21 Wind Speed Measurement Spatial & Temporal Variations of Wind Speed Height Z (m) Horizontal Distance tu (m) 21

22 Peak Factor of Wind Speed Peak Factor g U Ave Mean Wind Speed U (m/s) Power Spectrum of Wind Speed Power Spectral Density fs U (f) / σ 2 u Typhoon Frontal Depression 22

23 Schematic view of turbulence Turbulence Spectrum Inertial Range (Energy cascade) f S u (f) Production (Instability of mean flow) Dissipation (Viscosity) Large Eddies log f Small Eddies Cook,

24 Power Spectrum of Wind Speed (Fichtl-McVehill Model) f S u (f)) 4 f* = σ 2 u (1 + a f* f β ) 5 3β Gamma Function f L ux 4 β 1.5 (1/β ) β Γ(5/3β) f* * =, a = 1.5, b = U b β Γ(1/β) Γ(2/3β) β = 1 (Kaimal( Spectrum) β = 5/3 (Panofsky( Spectrum) β = 2 (Karman Spectrum) 5 f S u (f) f 3 (Kolmogorov s Hypothesis of Local Isotropy, Power of 5/3 Law in Inertial Subrange) Power Spectrum of Wind Speed Power Spectral Density fs U (f) / σ 2 u 24

25 Power Spectrum of Wind Speed (TTU) log{ f S u (f) /σ u 2 } log f (Tieleman, 1995) Power Spectrum of Wind Speed (Tieleman,1995) f S u (f) u * 2 = A f* γ (C + B f* f α ) β f Z f* * = U Z = Height α = 1, β = 5/3, γ = 1 (Blunt Model) α = 5/3, β =1, γ = 1 (Pointed Model) 25

26 Power Spectrum of Wind Speed (Typhoon 9119) Power Spectral Density fs U (f) / σ 2 u Before eye passing over : 90min After eye passing over : 110min Turbulence Scale Average Scale of Fluctuation L ux ux R uu (x)dx R uu = U R uu (τ )dτ uu (x)) : Spatial Correlation Coefficient of u(t) = u(r,t )u(r r + x,t x ) /σ 2 u uu (τ ) : Auto-correlation Coefficient of u(t) = u(r,t )u(r,t t + +τ ) /σ 2 u R uu 0 0 } Taylor s Hypothesis of Frozen Turbulence u(r, t ) u(r+ x, t ) x 26

27 Turbulence Scale Average Scale of Fluctuation Spatial Correlation Coefficient R uu (x) u(r,t ) u(r + x, t) x 1 L ux = 0 0 x L ux R uu (x)dx Turbulence Scale Wiener-Khintchine Relation S u (f) /σ 2 u = R uu (τ )exp( i 2π fτ )dτ S u (0) /σ 2 u = 2 2 R uu (τ )dτ = 2L ux / U 0 Turbulence Scale L ux = US u (0) / 2σ 2 u Isotropic Turbulence Field L ux = 2L2 uy = 2L2 uz (Near Ground: L ux 3L uz ) 27

28 Turbulence Scale (TTU) Garg,, et al., 1995 Turbulence Scale (AIJ Rec.1993) 200 Height Z (m) Z ux = 100( ) α 30 L ux L ux (m) 28

29 Correlation of Wind Speed (Root Coherence) Coherence f Z Reduced Frequency U missing!! Correlation of Wind Speed (Root Coherence) k 2 y y 2 +k 2 z z 2 Coherence exp ( f ) U 1 U 2 z U 1 (t)) = U 1 +u 1 (t) y U 2 (t)) = U 2 +u 2 (t) 29

Wind Resistant Design AIJ Recommendations for Wind Loads on Buildings

Wind Resistant Design AIJ Recommendations for Wind Loads on Buildings Lecture 6 Wind Resistant Design AIJ Recommendations for Wind Loads on Buildings Tokyo Polytechnic University The 1st Century Center of Excellence Program Yukio Tamura Background Building Standard Law of

More information

Eddy viscosity. AdOc 4060/5060 Spring 2013 Chris Jenkins. Turbulence (video 1hr):

Eddy viscosity. AdOc 4060/5060 Spring 2013 Chris Jenkins. Turbulence (video 1hr): AdOc 4060/5060 Spring 2013 Chris Jenkins Eddy viscosity Turbulence (video 1hr): http://cosee.umaine.edu/programs/webinars/turbulence/?cfid=8452711&cftoken=36780601 Part B Surface wind stress Wind stress

More information

ESS Turbulence and Diffusion in the Atmospheric Boundary-Layer : Winter 2017: Notes 1

ESS Turbulence and Diffusion in the Atmospheric Boundary-Layer : Winter 2017: Notes 1 ESS5203.03 - Turbulence and Diffusion in the Atmospheric Boundary-Layer : Winter 2017: Notes 1 Text: J.R.Garratt, The Atmospheric Boundary Layer, 1994. Cambridge Also some material from J.C. Kaimal and

More information

Examples of Pressure Gradient. Pressure Gradient Force. Chapter 7: Forces and Force Balances. Forces that Affect Atmospheric Motion 2/2/2015

Examples of Pressure Gradient. Pressure Gradient Force. Chapter 7: Forces and Force Balances. Forces that Affect Atmospheric Motion 2/2/2015 Chapter 7: Forces and Force Balances Forces that Affect Atmospheric Motion Fundamental force - Apparent force - Pressure gradient force Gravitational force Frictional force Centrifugal force Forces that

More information

Examples of Pressure Gradient. Pressure Gradient Force. Chapter 7: Forces and Force Balances. Forces that Affect Atmospheric Motion 2/7/2019

Examples of Pressure Gradient. Pressure Gradient Force. Chapter 7: Forces and Force Balances. Forces that Affect Atmospheric Motion 2/7/2019 Chapter 7: Forces and Force Balances Forces that Affect Atmospheric Motion Fundamental force - Apparent force - Pressure gradient force Gravitational force Frictional force Centrifugal force Forces that

More information

Hurricanes are intense vortical (rotational) storms that develop over the tropical oceans in regions of very warm surface water.

Hurricanes are intense vortical (rotational) storms that develop over the tropical oceans in regions of very warm surface water. Hurricanes: Observations and Dynamics Houze Section 10.1. Holton Section 9.7. Emanuel, K. A., 1988: Toward a general theory of hurricanes. American Scientist, 76, 371-379 (web link). http://ww2010.atmos.uiuc.edu/(gh)/guides/mtr/hurr/home.rxml

More information

ESCI 485 Air/sea Interaction Lesson 2 Turbulence Dr. DeCaria

ESCI 485 Air/sea Interaction Lesson 2 Turbulence Dr. DeCaria ESCI 485 Air/sea Interaction Lesson Turbulence Dr. DeCaria References: Air-sea Interaction: Laws and Mechanisms, Csanady An Introduction to Dynamic Meteorology ( rd edition), J.R. Holton An Introduction

More information

The dynamics of high and low pressure systems

The dynamics of high and low pressure systems The dynamics of high and low pressure systems Newton s second law for a parcel of air in an inertial coordinate system (a coordinate system in which the coordinate axes do not change direction and are

More information

DAY 19: Boundary Layer

DAY 19: Boundary Layer DAY 19: Boundary Layer flat plate : let us neglect the shape of the leading edge for now flat plate boundary layer: in blue we highlight the region of the flow where velocity is influenced by the presence

More information

Logarithmic velocity profile in the atmospheric (rough wall) boundary layer

Logarithmic velocity profile in the atmospheric (rough wall) boundary layer Logarithmic velocity profile in the atmospheric (rough wall) boundary layer P =< u w > U z = u 2 U z ~ ε = u 3 /kz Mean velocity profile in the Atmospheric Boundary layer Experimentally it was found that

More information

Lecture 2 Atmospheric Boundary Layer

Lecture 2 Atmospheric Boundary Layer Lecture Atmospheric Boundary Layer H. J. Fernando Ariona State niversity Region of the lower atmosphere where effects of the Earth surface are felt Surface fluxes of momentum, buoyancy.. Neutral, Convective,

More information

EART164: PLANETARY ATMOSPHERES

EART164: PLANETARY ATMOSPHERES EART164: PLANETARY ATMOSPHERES Francis Nimmo Last Week Radiative Transfer Black body radiation, Planck function, Wien s law Absorption, emission, opacity, optical depth Intensity, flux Radiative diffusion,

More information

Introduction to Meteorology & Climate. Climate & Earth System Science. Atmosphere Ocean Interactions. A: Structure of the Ocean.

Introduction to Meteorology & Climate. Climate & Earth System Science. Atmosphere Ocean Interactions. A: Structure of the Ocean. Climate & Earth System Science Introduction to Meteorology & Climate MAPH 10050 Peter Lynch Peter Lynch Meteorology & Climate Centre School of Mathematical Sciences University College Dublin Meteorology

More information

Chuichi Arakawa Graduate School of Interdisciplinary Information Studies, the University of Tokyo. Chuichi Arakawa

Chuichi Arakawa Graduate School of Interdisciplinary Information Studies, the University of Tokyo. Chuichi Arakawa Direct Numerical Simulations of Fundamental Turbulent Flows with the Largest Grid Numbers in the World and its Application of Modeling for Engineering Turbulent Flows Project Representative Chuichi Arakawa

More information

Reynolds Averaging. We separate the dynamical fields into slowly varying mean fields and rapidly varying turbulent components.

Reynolds Averaging. We separate the dynamical fields into slowly varying mean fields and rapidly varying turbulent components. Reynolds Averaging Reynolds Averaging We separate the dynamical fields into sloly varying mean fields and rapidly varying turbulent components. Reynolds Averaging We separate the dynamical fields into

More information

Turbulence Modeling I!

Turbulence Modeling I! Outline! Turbulence Modeling I! Grétar Tryggvason! Spring 2010! Why turbulence modeling! Reynolds Averaged Numerical Simulations! Zero and One equation models! Two equations models! Model predictions!

More information

Dynamics Rotating Tank

Dynamics Rotating Tank Institute for Atmospheric and Climate Science - IACETH Atmospheric Physics Lab Work Dynamics Rotating Tank Large scale flows on different latitudes of the rotating Earth Abstract The large scale atmospheric

More information

A note concerning the Lighthill sandwich model of tropical cyclones

A note concerning the Lighthill sandwich model of tropical cyclones Applied Mathematics A note concerning the Lighthill sandwich model of tropical cyclones G.I. Barenblatt, A.J. Chorin, V.M. Prostokishin The authors dedicate this work to the glowing memory of the great

More information

Weather and Climate Basics

Weather and Climate Basics Weather and Climate Basics Laura Boekel Forecaster at Bureau of Meteorology Aims of this presentation To describe what I do as a forecaster at the Bureau of Meteorology To provide an interesting introduction

More information

Weather and Climate Basics

Weather and Climate Basics Aims of this presentation Weather and Climate Basics To describe what I do as a forecaster at the Bureau of Meteorology Laura Boekel Forecaster at Bureau of Meteorology To provide an interesting introduction

More information

Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace

Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace Adapted from Publisher: John S. Wiley & Sons 2002 Center for Scientific Computation and

More information

Atm S 547 Boundary Layer Meteorology

Atm S 547 Boundary Layer Meteorology Lecture 5. The logarithmic sublayer and surface roughness In this lecture Similarity theory for the logarithmic sublayer. Characterization of different land and water surfaces for surface flux parameterization

More information

ADAPTATION OF THE REYNOLDS STRESS TURBULENCE MODEL FOR ATMOSPHERIC SIMULATIONS

ADAPTATION OF THE REYNOLDS STRESS TURBULENCE MODEL FOR ATMOSPHERIC SIMULATIONS ADAPTATION OF THE REYNOLDS STRESS TURBULENCE MODEL FOR ATMOSPHERIC SIMULATIONS Radi Sadek 1, Lionel Soulhac 1, Fabien Brocheton 2 and Emmanuel Buisson 2 1 Laboratoire de Mécanique des Fluides et d Acoustique,

More information

Dust devils, water spouts, tornados

Dust devils, water spouts, tornados Balanced flow Things we know Primitive equations are very comprehensive, but there may be a number of vast simplifications that may be relevant (e.g., geostrophic balance). Seems that there are things

More information

Extreme Winds in the Western North Pacific. Søren Ott

Extreme Winds in the Western North Pacific. Søren Ott in the Western North Pacific Søren Ott Outline Tropical cyclones and wind turbines Modelling extreme winds Validation Conclusions Cat. 4 tropical cyclone IVAN 15 Sept 2004 at landfall near Luisiana, USA

More information

BOUNDARY-LAYER METEOROLOGY

BOUNDARY-LAYER METEOROLOGY BOUNDARY-LAYER METEOROLOGY Han van Dop, September 2008 D 08-01 Contents 1 INTRODUCTION 3 1.1 Atmospheric thermodynamics.................... 3 1.2 Statistical aspects of fluid mechanics................

More information

The Equations of Motion in a Rotating Coordinate System. Chapter 3

The Equations of Motion in a Rotating Coordinate System. Chapter 3 The Equations of Motion in a Rotating Coordinate System Chapter 3 Since the earth is rotating about its axis and since it is convenient to adopt a frame of reference fixed in the earth, we need to study

More information

Chapter 1. Introduction

Chapter 1. Introduction Chapter 1. Introduction In this class, we will examine atmospheric phenomena that occurs at the mesoscale, including some boundary layer processes, convective storms, and hurricanes. We will emphasize

More information

(Wind profile) Chapter five. 5.1 The Nature of Airflow over the surface:

(Wind profile) Chapter five. 5.1 The Nature of Airflow over the surface: Chapter five (Wind profile) 5.1 The Nature of Airflow over the surface: The fluid moving over a level surface exerts a horizontal force on the surface in the direction of motion of the fluid, such a drag

More information

Direct and Large Eddy Simulation of stably stratified turbulent Ekman layers

Direct and Large Eddy Simulation of stably stratified turbulent Ekman layers Direct and Large Eddy Simulation of stably stratified turbulent Ekman layers Stimit Shah, Elie Bou-Zeid Princeton University 64 th APS DFD Baltimore, Maryland Nov 21, 211 Effect of Stability on Atmospheric

More information

Introduction to Mesoscale Meteorology

Introduction to Mesoscale Meteorology Introduction to Mesoscale Meteorology Overview Scale Definitions Synoptic Synoptic derived from Greek synoptikos meaning general view of the whole. Also has grown to imply at the same time or simultaneous.

More information

Go With the Flow From High to Low Investigating Isobars

Go With the Flow From High to Low Investigating Isobars Go With the Flow From High to Low Investigating Isobars Science 10 Mrs. Purba Air Masses The air over a warm surface can be heated, causing it to rise above more dense air. The result is the formation

More information

The effect of turbulence and gust on sand erosion and dust entrainment during sand storm Xue-Ling Cheng, Fei Hu and Qing-Cun Zeng

The effect of turbulence and gust on sand erosion and dust entrainment during sand storm Xue-Ling Cheng, Fei Hu and Qing-Cun Zeng The effect of turbulence and gust on sand erosion and dust entrainment during sand storm Xue-Ling Cheng, Fei Hu and Qing-Cun Zeng State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric

More information

Transient and Eddy. Transient/Eddy Flux. Flux Components. Lecture 3: Weather/Disturbance. Transient: deviations from time mean Time Mean

Transient and Eddy. Transient/Eddy Flux. Flux Components. Lecture 3: Weather/Disturbance. Transient: deviations from time mean Time Mean Lecture 3: Weather/Disturbance Transients and Eddies Climate Roles Mid-Latitude Cyclones Tropical Hurricanes Mid-Ocean Eddies Transient and Eddy Transient: deviations from time mean Time Mean Eddy: deviations

More information

Part I: Overview of modeling concepts and techniques Part II: Modeling neutrally stratified boundary layer flows

Part I: Overview of modeling concepts and techniques Part II: Modeling neutrally stratified boundary layer flows Physical modeling of atmospheric boundary layer flows Part I: Overview of modeling concepts and techniques Part II: Modeling neutrally stratified boundary layer flows Outline Evgeni Fedorovich School of

More information

Chapter (3) TURBULENCE KINETIC ENERGY

Chapter (3) TURBULENCE KINETIC ENERGY Chapter (3) TURBULENCE KINETIC ENERGY 3.1 The TKE budget Derivation : The definition of TKE presented is TKE/m= e = 0.5 ( u 2 + v 2 + w 2 ). we recognize immediately that TKE/m is nothing more than the

More information

Physical Modeling of the Atmospheric Boundary Layer in the University of New Hampshire s Flow Physics Facility

Physical Modeling of the Atmospheric Boundary Layer in the University of New Hampshire s Flow Physics Facility University of New Hampshire University of New Hampshire Scholars' Repository Honors Theses and Capstones Student Scholarship Spring 2016 Physical Modeling of the Atmospheric Boundary Layer in the University

More information

Vertical wind shear in relation to frequency of Monsoon Depressions and Tropical Cyclones of Indian Seas

Vertical wind shear in relation to frequency of Monsoon Depressions and Tropical Cyclones of Indian Seas Vertical wind shear in relation to frequency of Monsoon Depressions and Tropical Cyclones of Indian Seas Prince K. Xavier and P.V. Joseph Department of Atmospheric Sciences Cochin University of Science

More information

BIAS ON THE WIND-SPEED GUST CAUSED BY QUANTIZATION AND DISJUNCT SAMPLING OF THE CUP-ANEMOMETER SIGNAL

BIAS ON THE WIND-SPEED GUST CAUSED BY QUANTIZATION AND DISJUNCT SAMPLING OF THE CUP-ANEMOMETER SIGNAL BIAS ON THE WIND-SPEED GUST CAUSED BY QUANTIZATION AND DISJUNCT SAMPLING OF THE CUP-ANEMOMETER SIGNAL Presentation of Main Results L. Kristensen & Ole Frost Hansen January 16, 7 We are here concerned with

More information

centrifugal acceleration, whose magnitude is r cos, is zero at the poles and maximum at the equator. This distribution of the centrifugal acceleration

centrifugal acceleration, whose magnitude is r cos, is zero at the poles and maximum at the equator. This distribution of the centrifugal acceleration Lecture 10. Equations of Motion Centripetal Acceleration, Gravitation and Gravity The centripetal acceleration of a body located on the Earth's surface at a distance from the center is the force (per unit

More information

Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,

Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h, Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =

More information

The atmosphere in motion: forces and wind. AT350 Ahrens Chapter 9

The atmosphere in motion: forces and wind. AT350 Ahrens Chapter 9 The atmosphere in motion: forces and wind AT350 Ahrens Chapter 9 Recall that Pressure is force per unit area Air pressure is determined by the weight of air above A change in pressure over some distance

More information

Roughness Sub Layers John Finnigan, Roger Shaw, Ned Patton, Ian Harman

Roughness Sub Layers John Finnigan, Roger Shaw, Ned Patton, Ian Harman Roughness Sub Layers John Finnigan, Roger Shaw, Ned Patton, Ian Harman 1. Characteristics of the Roughness Sub layer With well understood caveats, the time averaged statistics of flow in the atmospheric

More information

Module 9 Weather Systems

Module 9 Weather Systems Module 9 Weather Systems In this module the theory of atmospheric dynamics is applied to different weather phenomena. The first section deals with extratropical cyclones, low and high pressure areas of

More information

Fundamentals of Weather and Climate

Fundamentals of Weather and Climate Fundamentals of Weather and Climate ROBIN McILVEEN Environmental Science Division Institute of Environmental and Biological Sciences Lancaster University CHAPMAN & HALL London Glasgow Weinheim New York

More information

Turbulence - Theory and Modelling GROUP-STUDIES:

Turbulence - Theory and Modelling GROUP-STUDIES: Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 046-0480 Johan Revstedt, tel 046-43 0 Turbulence - Theory and Modelling GROUP-STUDIES: Turbulence

More information

p = ρrt p = ρr d = T( q v ) dp dz = ρg

p = ρrt p = ρr d = T( q v ) dp dz = ρg Chapter 1: Properties of the Atmosphere What are the major chemical components of the atmosphere? Atmospheric Layers and their major characteristics: Troposphere, Stratosphere Mesosphere, Thermosphere

More information

Dynamic Meteorology - Introduction

Dynamic Meteorology - Introduction Dynamic Meteorology - Introduction Atmospheric dynamics the study of atmospheric motions that are associated with weather and climate We will consider the atmosphere to be a continuous fluid medium, or

More information

Introduction to Turbulence and Turbulence Modeling

Introduction to Turbulence and Turbulence Modeling Introduction to Turbulence and Turbulence Modeling Part I Venkat Raman The University of Texas at Austin Lecture notes based on the book Turbulent Flows by S. B. Pope Turbulent Flows Turbulent flows Commonly

More information

Section 13-1: Thunderstorms

Section 13-1: Thunderstorms Section 13-1: Thunderstorms Chapter 13 Main Idea: The intensity and duration of thunderstorms depend on the local conditions that create them. Air-mass thunderstorm Mountain thunderstorm Sea-breeze thunderstorm

More information

WQMAP (Water Quality Mapping and Analysis Program) is a proprietary. modeling system developed by Applied Science Associates, Inc.

WQMAP (Water Quality Mapping and Analysis Program) is a proprietary. modeling system developed by Applied Science Associates, Inc. Appendix A. ASA s WQMAP WQMAP (Water Quality Mapping and Analysis Program) is a proprietary modeling system developed by Applied Science Associates, Inc. and the University of Rhode Island for water quality

More information

d v 2 v = d v d t i n where "in" and "rot" denote the inertial (absolute) and rotating frames. Equation of motion F =

d v 2 v = d v d t i n where in and rot denote the inertial (absolute) and rotating frames. Equation of motion F = Governing equations of fluid dynamics under the influence of Earth rotation (Navier-Stokes Equations in rotating frame) Recap: From kinematic consideration, d v i n d t i n = d v rot d t r o t 2 v rot

More information

Bias on Horizontal Mean-Wind Speed and Variance caused by Turbulence

Bias on Horizontal Mean-Wind Speed and Variance caused by Turbulence Bias on Horizontal Mean-Wind Speed and Variance caused by Turbulence Presentation of Main Results Leif Kristensen & Ole Frost Hansen December 6, 2005 The cup anemometer is characterized by five, wind-speed

More information

Control Volume. Dynamics and Kinematics. Basic Conservation Laws. Lecture 1: Introduction and Review 1/24/2017

Control Volume. Dynamics and Kinematics. Basic Conservation Laws. Lecture 1: Introduction and Review 1/24/2017 Lecture 1: Introduction and Review Dynamics and Kinematics Kinematics: The term kinematics means motion. Kinematics is the study of motion without regard for the cause. Dynamics: On the other hand, dynamics

More information

Lecture 1: Introduction and Review

Lecture 1: Introduction and Review Lecture 1: Introduction and Review Review of fundamental mathematical tools Fundamental and apparent forces Dynamics and Kinematics Kinematics: The term kinematics means motion. Kinematics is the study

More information

Note the diverse scales of eddy motion and self-similar appearance at different lengthscales of the turbulence in this water jet. Only eddies of size

Note the diverse scales of eddy motion and self-similar appearance at different lengthscales of the turbulence in this water jet. Only eddies of size L Note the diverse scales of eddy motion and self-similar appearance at different lengthscales of the turbulence in this water jet. Only eddies of size 0.01L or smaller are subject to substantial viscous

More information

Chapter 7 The Time-Dependent Navier-Stokes Equations Turbulent Flows

Chapter 7 The Time-Dependent Navier-Stokes Equations Turbulent Flows Chapter 7 The Time-Dependent Navier-Stokes Equations Turbulent Flows Remark 7.1. Turbulent flows. The usually used model for turbulent incompressible flows are the incompressible Navier Stokes equations

More information

Guided Notes: Atmosphere Layers of the Atmosphere

Guided Notes: Atmosphere Layers of the Atmosphere Guided Notes: Atmosphere Layers of the Atmosphere Atmosphere: Absorbs solar radiation, Burns up meteors, transports and recycles water, and other chemicals, and moderates climate Main Components: o Meteorology

More information

General Atmospheric Circulation

General Atmospheric Circulation General Atmospheric Circulation Take away Concepts and Ideas Global circulation: The mean meridional (N-S) circulation Trade winds and westerlies The Jet Stream Earth s climate zones Monsoonal climate

More information

Chapter 7. Basic Turbulence

Chapter 7. Basic Turbulence Chapter 7 Basic Turbulence The universe is a highly turbulent place, and we must understand turbulence if we want to understand a lot of what s going on. Interstellar turbulence causes the twinkling of

More information

Measurement of Rotation. Circulation. Example. Lecture 4: Circulation and Vorticity 1/31/2017

Measurement of Rotation. Circulation. Example. Lecture 4: Circulation and Vorticity 1/31/2017 Lecture 4: Circulation and Vorticity Measurement of Rotation Circulation Bjerknes Circulation Theorem Vorticity Potential Vorticity Conservation of Potential Vorticity Circulation and vorticity are the

More information

Vertical Structure of Atmosphere

Vertical Structure of Atmosphere ATMOS 3110 Introduction to Atmospheric Sciences Distribution of atmospheric mass and gaseous constituents Because of the earth s gravitational field, the atmosphere exerts a downward forces on the earth

More information

The Atmospheric Boundary Layer. The Surface Energy Balance (9.2)

The Atmospheric Boundary Layer. The Surface Energy Balance (9.2) The Atmospheric Boundary Layer Turbulence (9.1) The Surface Energy Balance (9.2) Vertical Structure (9.3) Evolution (9.4) Special Effects (9.5) The Boundary Layer in Context (9.6) Fair Weather over Land

More information

(April 7, 2010, Wednesday) Tropical Storms & Hurricanes Part 2

(April 7, 2010, Wednesday) Tropical Storms & Hurricanes Part 2 Lecture #17 (April 7, 2010, Wednesday) Tropical Storms & Hurricanes Part 2 Hurricane Katrina August 2005 All tropical cyclone tracks (1945-2006). Hurricane Formation While moving westward, tropical disturbances

More information

Lecture 5: Atmospheric General Circulation and Climate

Lecture 5: Atmospheric General Circulation and Climate Lecture 5: Atmospheric General Circulation and Climate Geostrophic balance Zonal-mean circulation Transients and eddies Meridional energy transport Moist static energy Angular momentum balance Atmosphere

More information

4. Atmospheric transport. Daniel J. Jacob, Atmospheric Chemistry, Harvard University, Spring 2017

4. Atmospheric transport. Daniel J. Jacob, Atmospheric Chemistry, Harvard University, Spring 2017 4. Atmospheric transport Daniel J. Jacob, Atmospheric Chemistry, Harvard University, Spring 2017 Forces in the atmosphere: Gravity g Pressure-gradient ap = ( 1/ ρ ) dp / dx for x-direction (also y, z directions)

More information

1/18/2011. Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis ESS227 Prof. Jin-Yi Yu

1/18/2011. Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis ESS227 Prof. Jin-Yi Yu Lecture 2: Basic Conservation Laws Conservation Law of Momentum Newton s 2 nd Law of Momentum = absolute velocity viewed in an inertial system = rate of change of Ua following the motion in an inertial

More information

Storm and Storm Systems Related Vocabulary and Definitions. Magnitudes are measured differently for different hazard types:

Storm and Storm Systems Related Vocabulary and Definitions. Magnitudes are measured differently for different hazard types: Storm and Storm Systems Related Vocabulary and Definitions Magnitude: this is an indication of the scale of an event, often synonymous with intensity or size. In natural systems, magnitude is also related

More information

GEF 1100 Klimasystemet. Chapter 7: Balanced flow

GEF 1100 Klimasystemet. Chapter 7: Balanced flow GEF1100 Autumn 2016 27.09.2016 GEF 1100 Klimasystemet Chapter 7: Balanced flow Prof. Dr. Kirstin Krüger (MetOs, UiO) 1 Lecture Outline Ch. 7 Ch. 7 Balanced flow 1. Motivation 2. Geostrophic motion 2.1

More information

A Note on the Estimation of Eddy Diffusivity and Dissipation Length in Low Winds over a Tropical Urban Terrain

A Note on the Estimation of Eddy Diffusivity and Dissipation Length in Low Winds over a Tropical Urban Terrain Pure appl. geophys. 160 (2003) 395 404 0033 4553/03/020395 10 Ó Birkhäuser Verlag, Basel, 2003 Pure and Applied Geophysics A Note on the Estimation of Eddy Diffusivity and Dissipation Length in Low Winds

More information

Lecture 14. Turbulent Combustion. We know what a turbulent flow is, when we see it! it is characterized by disorder, vorticity and mixing.

Lecture 14. Turbulent Combustion. We know what a turbulent flow is, when we see it! it is characterized by disorder, vorticity and mixing. Lecture 14 Turbulent Combustion 1 We know what a turbulent flow is, when we see it! it is characterized by disorder, vorticity and mixing. In a fluid flow, turbulence is characterized by fluctuations of

More information

7. Basics of Turbulent Flow Figure 1.

7. Basics of Turbulent Flow Figure 1. 1 7. Basics of Turbulent Flow Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds

More information

The General Circulation of the Atmosphere: A Numerical Experiment

The General Circulation of the Atmosphere: A Numerical Experiment The General Circulation of the Atmosphere: A Numerical Experiment Norman A. Phillips (1956) Presentation by Lukas Strebel and Fabian Thüring Goal of the Model Numerically predict the mean state of the

More information

Hurricanes. April 14, 2009

Hurricanes. April 14, 2009 Tropical Weather & Hurricanes Chapter 15 April 14, 2009 Tropical meteorology Tropics characterized by seasonal wet and drier periods- wet when sun is nearly overhead at noon and inter-tropical convergence

More information

The Stable Boundary layer

The Stable Boundary layer The Stable Boundary layer the statistically stable or stratified regime occurs when surface is cooler than the air The stable BL forms at night over land (Nocturnal Boundary Layer) or when warm air travels

More information

Part-8c Circulation (Cont)

Part-8c Circulation (Cont) Part-8c Circulation (Cont) Global Circulation Means of Transfering Heat Easterlies /Westerlies Polar Front Planetary Waves Gravity Waves Mars Circulation Giant Planet Atmospheres Zones and Belts Global

More information

Atmospheric Pressure and Wind Frode Stordal, University of Oslo

Atmospheric Pressure and Wind Frode Stordal, University of Oslo Chapter 4 Lecture Understanding Weather and Climate Seventh Edition Atmospheric Pressure and Wind Frode Stordal, University of Oslo Redina L. Herman Western Illinois University The Concept of Pressure

More information

Answers to Homework #9

Answers to Homework #9 Answers to Homework #9 Problem 1: 1. We want to express the kinetic energy per unit wavelength E(k), of dimensions L 3 T 2, as a function of the local rate of energy dissipation ɛ, of dimensions L 2 T

More information

On the validation study devoted to stratified atmospheric flow over an isolated hill

On the validation study devoted to stratified atmospheric flow over an isolated hill On the validation study devoted to stratified atmospheric flow over an isolated hill Sládek I. 2/, Kozel K. 1/, Jaňour Z. 2/ 1/ U1211, Faculty of Mechanical Engineering, Czech Technical University in Prague.

More information

Atmospheric Fronts. The material in this section is based largely on. Lectures on Dynamical Meteorology by Roger Smith.

Atmospheric Fronts. The material in this section is based largely on. Lectures on Dynamical Meteorology by Roger Smith. Atmospheric Fronts The material in this section is based largely on Lectures on Dynamical Meteorology by Roger Smith. Atmospheric Fronts 2 Atmospheric Fronts A front is the sloping interfacial region of

More information

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) The ABL, though turbulent, is not homogeneous, and a critical role of turbulence is transport and mixing of air properties, especially in the

More information

2.3 The Turbulent Flat Plate Boundary Layer

2.3 The Turbulent Flat Plate Boundary Layer Canonical Turbulent Flows 19 2.3 The Turbulent Flat Plate Boundary Layer The turbulent flat plate boundary layer (BL) is a particular case of the general class of flows known as boundary layer flows. The

More information

Chapter 24. Tropical Cyclones. Tropical Cyclone Classification 4/19/17

Chapter 24. Tropical Cyclones. Tropical Cyclone Classification 4/19/17 Chapter 24 Tropical Cyclones Tropical Cyclones Most destructive storms on the planet Originate over tropical waters, but their paths often take them over land and into midlatitudes Names Hurricane (Atlantic

More information

A Discussion on The Effect of Mesh Resolution on Convective Boundary Layer Statistics and Structures Generated by Large-Eddy Simulation by Sullivan

A Discussion on The Effect of Mesh Resolution on Convective Boundary Layer Statistics and Structures Generated by Large-Eddy Simulation by Sullivan 耶鲁 - 南京信息工程大学大气环境中心 Yale-NUIST Center on Atmospheric Environment A Discussion on The Effect of Mesh Resolution on Convective Boundary Layer Statistics and Structures Generated by Large-Eddy Simulation

More information

Contents. Parti Fundamentals. 1. Introduction. 2. The Coriolis Force. Preface Preface of the First Edition

Contents. Parti Fundamentals. 1. Introduction. 2. The Coriolis Force. Preface Preface of the First Edition Foreword Preface Preface of the First Edition xiii xv xvii Parti Fundamentals 1. Introduction 1.1 Objective 3 1.2 Importance of Geophysical Fluid Dynamics 4 1.3 Distinguishing Attributes of Geophysical

More information

Mesoscale meteorological models. Claire L. Vincent, Caroline Draxl and Joakim R. Nielsen

Mesoscale meteorological models. Claire L. Vincent, Caroline Draxl and Joakim R. Nielsen Mesoscale meteorological models Claire L. Vincent, Caroline Draxl and Joakim R. Nielsen Outline Mesoscale and synoptic scale meteorology Meteorological models Dynamics Parametrizations and interactions

More information

Dynamic Meteorology (lecture 13, 2016)

Dynamic Meteorology (lecture 13, 2016) Dynamic Meteorology (lecture 13, 2016) Topics Chapter 3, lecture notes: High frequency waves (no rota;on) Boussinesq approxima4on Normal mode analysis of the stability of hydrosta4c balance Buoyancy waves

More information

Atmospheric dynamics and meteorology

Atmospheric dynamics and meteorology Atmospheric dynamics and meteorology B. Legras, http://www.lmd.ens.fr/legras III Frontogenesis (pre requisite: quasi-geostrophic equation, baroclinic instability in the Eady and Phillips models ) Recommended

More information

Lecture 1. Equations of motion - Newton s second law in three dimensions. Pressure gradient + force force

Lecture 1. Equations of motion - Newton s second law in three dimensions. Pressure gradient + force force Lecture 3 Lecture 1 Basic dynamics Equations of motion - Newton s second law in three dimensions Acceleration = Pressure Coriolis + gravity + friction gradient + force force This set of equations is the

More information

Weather is the of the Earth s atmosphere at a place and time. It is the movement of through the atmosphere o Energy comes from the

Weather is the of the Earth s atmosphere at a place and time. It is the movement of through the atmosphere o Energy comes from the Weather Notes Weather Weather is the of the Earth s atmosphere at a place and time It is the movement of through the atmosphere o Energy comes from the The sun is the force that weather The sun s energy

More information

1/3/2011. This course discusses the physical laws that govern atmosphere/ocean motions.

1/3/2011. This course discusses the physical laws that govern atmosphere/ocean motions. Lecture 1: Introduction and Review Dynamics and Kinematics Kinematics: The term kinematics means motion. Kinematics is the study of motion without regard for the cause. Dynamics: On the other hand, dynamics

More information

Tropical Cyclones. Objectives

Tropical Cyclones. Objectives Tropical Cyclones FIU Undergraduate Hurricane Internship Lecture 2 8/8/2012 Objectives From this lecture you should understand: Global tracks of TCs and the seasons when they are most common General circulation

More information

Applied Computational Fluid Dynamics

Applied Computational Fluid Dynamics Lecture 9 - Kolmogorov s Theory Applied Computational Fluid Dynamics Instructor: André Bakker André Bakker (2002-2005) Fluent Inc. (2002) 1 Eddy size Kolmogorov s theory describes how energy is transferred

More information

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing.

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Thus, it is very important to form both a conceptual understanding and a quantitative

More information

Lecture 12. The diurnal cycle and the nocturnal BL

Lecture 12. The diurnal cycle and the nocturnal BL Lecture 12. The diurnal cycle and the nocturnal BL Over flat land, under clear skies and with weak thermal advection, the atmospheric boundary layer undergoes a pronounced diurnal cycle. A schematic and

More information

LECTURE 28. The Planetary Boundary Layer

LECTURE 28. The Planetary Boundary Layer LECTURE 28 The Planetary Boundary Layer The planetary boundary layer (PBL) [also known as atmospheric boundary layer (ABL)] is the lower part of the atmosphere in which the flow is strongly influenced

More information

Influence of forced near-inertial motion on the kinetic energy of a nearly-geostrophic flow

Influence of forced near-inertial motion on the kinetic energy of a nearly-geostrophic flow Abstract Influence of forced near-inertial motion on the kinetic energy of a nearly-geostrophic flow Stephanne Taylor and David Straub McGill University stephanne.taylor@mail.mcgill.ca The effect of forced

More information

Outline: Phenomenology of Wall Bounded Turbulence: Minimal Models First Story: Large Re Neutrally-Stratified (NS) Channel Flow.

Outline: Phenomenology of Wall Bounded Turbulence: Minimal Models First Story: Large Re Neutrally-Stratified (NS) Channel Flow. Victor S. L vov: Israeli-Italian March 2007 Meeting Phenomenology of Wall Bounded Turbulence: Minimal Models In collaboration with : Anna Pomyalov, Itamar Procaccia, Oleksii Rudenko (WIS), Said Elgobashi

More information

Class exercises Chapter 3. Elementary Applications of the Basic Equations

Class exercises Chapter 3. Elementary Applications of the Basic Equations Class exercises Chapter 3. Elementary Applications of the Basic Equations Section 3.1 Basic Equations in Isobaric Coordinates 3.1 For some (in fact many) applications we assume that the change of the Coriolis

More information

Donald Slinn, Murray D. Levine

Donald Slinn, Murray D. Levine 2 Donald Slinn, Murray D. Levine 2 Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis,

More information