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

Save this PDF as:
Size: px
Start display at page:

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

## Transcription

1 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 starting point for discussions of the circulation of a fluid in a thin spherical shell on a rotating sphere. 1

2 3.1 Horizontal force balance - geostrophic balance Away from boundaries and on timescales longer than a day the atmosphere and ocean are in geostrophic balance: Pressure gradient force + Coriolis force = 0 Re-arranging leads to the definition of geostrophic winds (or geostrophic currents): On a rotating planet fluid does not flow from high to low pressure, but along contours of constant pressure! The effect of Coriolis deflecting flow to the right (in the Northern hemisphere) is balanced by the horizontal component of the pressure gradient force from high to low pressure. Geostrophic flow around high and low pressure centres (Northern hemisphere). 2

3 500 mb pressure contours and wind vectors Buys-Ballots Law If you ve got your back to the wind, the low pressure is to your left (northern hemisphere). Gulf Stream rings - which way does the ocean circulate around these warm and cold core eddies? warm core high sea-level cold core low sea-level 3

4 At the surface, air parcels actually move at an angle to isobars due to surface roughness which introduces friction. Three-way force balance: Pressure gradient force + Coriolis force + friction = 0 P = const Low pressure is still to the left of the wind, but there is also a frictionally-induced component down the pressure gradient. As a result, wind spirals into low pressure centres, and out of high pressure centres. 4

5 Air flows cyclonically around low pressure systems. This is anticlockwise in the northern hemisphere, and clockwise in the southern hemisphere. 5

6 3.2 Vertical force balance - hydrostatic balance The dominant balance in the vertical direction is between the pressure gradient force and gravity: pressure gradient force Hydrostatic balance: gravity Since P 0 as z (the atmosphere fades away at the top) the pressure at any height z is given by: Pressure = weight of air (or ocean plus air!) in the vertical column of unit cross-sectional area above any given point. Pressure gradient force If the mass of the Earth s atmosphere were uniformly distributed, pressure at sea-level would be x 10 5 Pa = 1013 hpa = 1 atm = 1 bar. 6

7 3.3 Equation of state for a dry atmosphere All gases obey the Ideal Gas Law: Here, the temperature T is in Kelvin, and R = R g /m a = 287 J kg -1 K -1, where R g is the universal gas constant J K -1 mol -1, and m a is the mean molecular weight of dry air, x 10-3 kg mol -1. At standard temperature (273K) and pressure (1013 hpa), ρ = kg m -3. Air is compressible, and has a relatively large thermal expansion coefficient. Substituting the equation of state into the hydrostatic relation gives: If T = T 0 then: where the scale height if P = P S at z = 0. Pressure decreases exponentially with height, with e-folding scale H. 7

8 For the troposphere, T 0 ~ 250K and H = 7.3km. The pressure is equal to 100hPa (1/10 of the surface pressure) at a height or 16.8 km. Density profile given by: 3.4 Equation of state for the ocean No exact analytical expression exists for the density of the ocean, which depends nonlinearly on T, S and P: However, it has been determined empirically to better than 1 part in The mean density of the ocean is 1035 kg m -3, and the density varies by less than 7%. This means that: 10m depth of water exerts a pressure of about 10 5 Pa or 1 atm. Pressure varies approximately linearly with depth in the ocean. It is convenient to define: [kg m -3 ] 8

9 Salinity - a measure of the amount of salt dissolved in water. Modern salinity measurements are dimensionless - the Practical Salinity Scale defines salinity in terms of a conductivity ratio that is very nearly equal to g kg -1 (or ). 1 kg of seawater typically has approximately 34.5g of dissolved salts (S = 34.5 psu = 34.5 g kg -1 = 34.5 ). 9

10 Seawater is almost (but not quite!) incompressible. It is helpful to remove the direct effect of pressure by evaluating σ at atmospheric pressure P a. which varies from 23 to 28 kg m -3 across the global ocean. The TS diagram - density (σ t ) as a function of temperature and salinity Isopycnals Temp ( o C) Salinity (psu) 10

11 For many purposes we can use a simplified equation of state, where density is linearized about a reference density ρ 0, corresponding to temperature T 0 and salinity S 0. (S 0,T 0 ) Typically α = 2 x 10-4 K -1 and β = 8 x 10-4 ( ) Potential temperature An air parcel moved from the surface upwards will expand and cool. Even though no heat is added to or removed from it, the temperature still changes, because the atmosphere is compressible. Therefore it is useful to define the: potential temperature (θ) = the temperature a fluid parcel would have if it were brought adiabatically to the surface. without exchanging any heat with its surroundings. Unless heat is added, fluid parcels conserve θ. 11

12 Potential temperature on a meridional transect through the Atlantic. Salinity on a meridional transect through the Atlantic. 12

13 3.6 Thermal wind balance Geostrophic and hydrostatic balance can be combined to tell us how the geostrophic flow varies with height. For the ocean, where ρ ρ 0 : Using the hydrostatic equation: Thermal wind equations Wherever there are horizontal density gradients, the horizontal flow must change with height. e.g. the Gulf Stream in the North Atlantic potential temperature (θ) density (σ t ) northward velocity 13

14 V e.g. cross-sections of velocity and temperature across the Florida Straits northward velocity ϑ Isotherms isopycnals Leaman et al. (1987) In the atmosphere ρ is a function of z so the equations and derivation are slightly different. In pressure coordinates thermal wind balance can be written: u warm (light). u=0 cold (dense) Equator y Pole 14

15 Zonal-mean zonal wind: There is a meridional gradient in atmospheric temperature. Thermal wind balance implies that the zonal wind must increase with height! Summary of key points To leading order, the large-scale ocean and atmosphere circulations are described by geostrophic and hydrostatic balance. Atmospheric pressure and density decay exponentially with height with an e-folding scale dependent on the temperature of the atmosphere. Ocean pressure varies approximately linearly with depth. Ocean density increases as salinity increases and temperature decreases, but the equation of state is nonlinear. In the absence of buoyancy forcing a fluid parcel conserves its potential temperature and salinity. The thermal wind equations embody geostrophic and hydrostatic balance and tell us that, wherever there is a horizontal temperature or density gradient, the horizontal flow must change with height. 15

### ( ) = 1005 J kg 1 K 1 ;

Problem Set 3 1. A parcel of water is added to the ocean surface that is denser (heavier) than any of the waters in the ocean. Suppose the parcel sinks to the ocean bottom; estimate the change in temperature

### 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

### Lecture 10 March 15, 2010, Monday. Atmospheric Pressure & Wind: Part 1

Lecture 10 March 15, 2010, Monday Atmospheric Pressure & Wind: Part 1 Speed, Velocity, Acceleration, Force, Pressure Atmospheric Pressure & Its Measurement Ideal Gas Law (Equation of State) Pressure Gradient

### Ocean Currents and Climate

Ocean Currents and Climate Ocean water contains streamlike movements of water called ocean currents. Currents are influenced by a number of factors, including weather, the Earth's rotation, and the position

### 1. The vertical structure of the atmosphere. Temperature profile.

Lecture 4. The structure of the atmosphere. Air in motion. Objectives: 1. The vertical structure of the atmosphere. Temperature profile. 2. Temperature in the lower atmosphere: dry adiabatic lapse rate.

### Surface Circulation. Key Ideas

Surface Circulation The westerlies and the trade winds are two of the winds that drive the ocean s surface currents. 1 Key Ideas Ocean water circulates in currents. Surface currents are caused mainly by

### 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

### Lecture 2. Lecture 1. Forces on a rotating planet. We will describe the atmosphere and ocean in terms of their:

Lecture 2 Lecture 1 Forces on a rotating planet We will describe the atmosphere and ocean in terms of their: velocity u = (u,v,w) pressure P density ρ temperature T salinity S up For convenience, we will

### SIO 210 Introduction to Physical Oceanography Mid-term examination November 3, 2014; 1 hour 20 minutes

NAME: SIO 210 Introduction to Physical Oceanography Mid-term examination November 3, 2014; 1 hour 20 minutes Closed book; one sheet of your own notes is allowed. A calculator is allowed. (100 total points.)

### psio 210 Introduction to Physical Oceanography Mid-term examination November 3, 2014; 1 hour 20 minutes Answer key

NAME: psio 210 Introduction to Physical Oceanography Mid-term examination November 3, 2014; 1 hour 20 minutes Answer key Closed book; one sheet of your own notes is allowed. A calculator is allowed. (100

### 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

### Winds and Currents in the Oceans

Winds and Currents in the Oceans Atmospheric Processes Density of air is controlled by temperature, pressure, and moisture content. 1. Warm air is less dense than cold air and moist air is less dense than

### 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

### The Behaviour of the Atmosphere

3 The Behaviour of the Atmosphere Learning Goals After studying this chapter, students should be able to: apply the ideal gas law and the concept of hydrostatic balance to the atmosphere (pp. 49 54); apply

### Lecture 12: Angular Momentum and the Hadley Circulation

Lecture 12: Angular Momentum and the Hadley Circulation September 30, 2003 We learnt last time that there is a planetary radiative drive net warming in the tropics, cooling over the pole which induces

### Conservation of Mass Conservation of Energy Scaling Analysis. ESS227 Prof. Jin-Yi Yu

Lecture 2: Basic Conservation Laws Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis Conservation Law of Momentum Newton s 2 nd Law of Momentum = absolute velocity viewed

### INTRODUCTION TO METEOROLOGY PART TWO SC 208 DECEMBER 2, 2014 JOHN BUSH

INTRODUCTION TO METEOROLOGY PART TWO SC 208 DECEMBER 2, 2014 JOHN BUSH Meteorology ATMOSPHERIC SCIENCES Short term weather systems in time spans of hours, days, weeks or months Emphasis is on forecasting

### 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

### Geostrophy & Thermal wind

Lecture 10 Geostrophy & Thermal wind 10.1 f and β planes These are planes that are tangent to the earth (taken to be spherical) at a point of interest. The z ais is perpendicular to the plane (anti-parallel

### ATS 421/521. Climate Modeling. Spring 2015

ATS 421/521 Climate Modeling Spring 2015 Lecture 9 Hadley Circulation (Held and Hou, 1980) General Circulation Models (tetbook chapter 3.2.3; course notes chapter 5.3) The Primitive Equations (tetbook

### 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

### Winds and Global Circulation

Winds and Global Circulation Atmospheric Pressure Winds Global Wind and Pressure Patterns Oceans and Ocean Currents El Nino How is Energy Transported to its escape zones? Both atmospheric and ocean transport

### 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)

### Lecture 8. Lecture 1. Wind-driven gyres. Ekman transport and Ekman pumping in a typical ocean basin. VEk

Lecture 8 Lecture 1 Wind-driven gyres Ekman transport and Ekman pumping in a typical ocean basin. VEk wek > 0 VEk wek < 0 VEk 1 8.1 Vorticity and circulation The vorticity of a parcel is a measure of its

### Introduction to Atmospheric Circulation

Introduction to Atmospheric Circulation Start rotating table Cloud Fraction Dice Results from http://eos.atmos.washington.edu/erbe/ from http://eos.atmos.washington.edu/erbe/ from http://eos.atmos.washington.edu/erbe/

### Physical Oceanography, MSCI 3001 Oceanographic Processes, MSCI Dr. Katrin Meissner Ocean Dynamics.

Physical Oceanography, MSCI 3001 Oceanographic Processes, MSCI 5004 Dr. Katrin Meissner k.meissner@unsw.e.au Ocean Dynamics The Equations of Motion d u dt = 1 ρ Σ F dt = 1 ρ ΣF x dt = 1 ρ ΣF y dw dt =

### F = ma. ATS 150 Global Climate Change Winds and Weather. Scott Denning CSU CMMAP 1. Please read Chapter 6 from Archer Textbook

Winds and Weather Please read Chapter 6 from Archer Textbook Circulation of the atmosphere and oceans are driven by energy imbalances Energy Imbalances What Makes the Wind Blow? Three real forces (gravity,

### Lecture D15 - Gravitational Attraction. The Earth as a Non-Inertial Reference Frame

J. Peraire 16.07 Dynamics Fall 2004 Version 1.3 Lecture D15 - Gravitational Attraction. The Earth as a Non-Inertial Reference Frame Gravitational attraction The Law of Universal Attraction was already

### Ocean and Climate I.

Ocean and Climate I http://www.gerhardriessbeck.de/ Physical Characteristics of the Ocean Surface area: 3.61 10 14 m 2 Mean depth: 3.7 km Ocean volume: 3.2 10 17 m 3 Mean density: 1.035 10 3 kg/m 3 Ocean

### 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

### 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

### 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

### NWP Equations (Adapted from UCAR/COMET Online Modules)

NWP Equations (Adapted from UCAR/COMET Online Modules) Certain physical laws of motion and conservation of energy (for example, Newton's Second Law of Motion and the First Law of Thermodynamics) govern

### Dynamics and Kinematics

Geophysics Fluid Dynamics () Syllabus Course Time Lectures: Tu, Th 09:30-10:50 Discussion: 3315 Croul Hall Text Book J. R. Holton, "An introduction to Dynamic Meteorology", Academic Press (Ch. 1, 2, 3,

### General Circulation. Nili Harnik DEES, Lamont-Doherty Earth Observatory

General Circulation Nili Harnik DEES, Lamont-Doherty Earth Observatory nili@ldeo.columbia.edu Latitudinal Radiation Imbalance The annual mean, averaged around latitude circles, of the balance between the

### Geophysics Fluid Dynamics (ESS228)

Geophysics Fluid Dynamics (ESS228) Course Time Lectures: Tu, Th 09:30-10:50 Discussion: 3315 Croul Hall Text Book J. R. Holton, "An introduction to Dynamic Meteorology", Academic Press (Ch. 1, 2, 3, 4,

### Atmosphere, Ocean and Climate Dynamics Fall 2008

MIT OpenCourseWare http://ocw.mit.edu 12.003 Atmosphere, Ocean and Climate Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Problem

### 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

### General Comment on Lab Reports: v. good + corresponds to a lab report that: has structure (Intro., Method, Results, Discussion, an Abstract would be

General Comment on Lab Reports: v. good + corresponds to a lab report that: has structure (Intro., Method, Results, Discussion, an Abstract would be a bonus) is well written (take your time to edit) shows

### SIO 210 Introduction to Physical Oceanography Mid-term examination November 5, 2012; 50 minutes Answer key

SIO 210 Introduction to Physical Oceanography Mid-term examination November 5, 2012; 50 minutes Answer key Closed book; one sheet of your own notes is allowed. A calculator is allowed. (100 total points.)

### CHAPTER 2 - ATMOSPHERIC CIRCULATION & AIR/SEA INTERACTION

Chapter 2 - pg. 1 CHAPTER 2 - ATMOSPHERIC CIRCULATION & AIR/SEA INTERACTION The atmosphere is driven by the variations of solar heating with latitude. The heat is transferred to the air by direct absorption

### 2 Atmospheric Pressure

2 Atmospheric Pressure METEOROLOGY 2.1 Definition and Pressure Measurement 2.1.1 Definition Pressure acts in all directions, up and sideways as well as down, but it is convenient in meteorology to regard

### Atmosphere, Ocean and Climate Dynamics Answers to Chapter 8

Atmosphere, Ocean and Climate Dynamics Answers to Chapter 8 1. Consider a zonally symmetric circulation (i.e., one with no longitudinal variations) in the atmosphere. In the inviscid upper troposphere,

### 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

### 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

### 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

### 2. Conservation laws and basic equations

2. Conservation laws and basic equations Equatorial region is mapped well by cylindrical (Mercator) projection: eastward, northward, upward (local Cartesian) coordinates:,, velocity vector:,,,, material

### 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

### 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

### 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

### 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

### Hydrostatic Equation and Thermal Wind. Meteorology 411 Iowa State University Week 5 Bill Gallus

Hydrostatic Equation and Thermal Wind Meteorology 411 Iowa State University Week 5 Bill Gallus Hydrostatic Equation In the atmosphere, vertical accelerations (dw/dt) are normally fairly small, and we can

### Properties of the Ocean NOAA Tech Refresh 20 Jan 2012 Kipp Shearman, OSU

Properties of the Ocean NOAA Tech Refresh 20 Jan 2012 Kipp Shearman, OSU Kipp Shearman T ( C) May 05 10, 2006 Physical Oceanographer I am interested in all things coastal Lots of observations: big boats,

### warmest (coldest) temperatures at summer heat dispersed upward by vertical motion Prof. Jin-Yi Yu ESS200A heated by solar radiation at the base

Pole Eq Lecture 3: ATMOSPHERE (Outline) JS JP Hadley Cell Ferrel Cell Polar Cell (driven by eddies) L H L H Basic Structures and Dynamics General Circulation in the Troposphere General Circulation in the

### Temperature (T) degrees Celsius ( o C) arbitrary scale from 0 o C at melting point of ice to 100 o C at boiling point of water Also (Kelvin, K) = o C

1 2 3 4 Temperature (T) degrees Celsius ( o C) arbitrary scale from 0 o C at melting point of ice to 100 o C at boiling point of water Also (Kelvin, K) = o C plus 273.15 0 K is absolute zero, the minimum

### SIO 210 Introduction to Physical Oceanography Mid-term examination Wednesday, November 2, :00 2:50 PM

SIO 210 Introduction to Physical Oceanography Mid-term examination Wednesday, November 2, 2005 2:00 2:50 PM This is a closed book exam. Calculators are allowed. (101 total points.) MULTIPLE CHOICE (3 points

### True or false: The atmosphere is always in hydrostatic balance. A. True B. False

Clicker Questions and Clicker Quizzes Clicker Questions Chapter 7 Of the four forces that affect the motion of air in our atmosphere, which is to thank for opposing the vertical pressure gradient force

### ATMOSPHERE M E T E O R O LO G Y

1.05.01 ATMOSPHERE 1. 0 5 M E T E O R O LO G Y INTRODUCTION ATMOSPHERIC COMPOSITION The atmosphere of Earth is the layer of gases, commonly known as air, that surrounds the planet Earth and is retained

### Dynamics of the Zonal-Mean, Time-Mean Tropical Circulation

Dynamics of the Zonal-Mean, Time-Mean Tropical Circulation First consider a hypothetical planet like Earth, but with no continents and no seasons and for which the only friction acting on the atmosphere

### Temperature Pressure Wind Moisture

Chapter 1: Properties of Atmosphere Temperature Pressure Wind Moisture Thickness of the Atmosphere (from Meteorology Today) 90% 70% The thickness of the atmosphere is only about 2% of Earth s thickness

### Atmosphere, Ocean and Climate Dynamics Fall 2008

MIT OpenCourseWare http://ocw.mit.edu 12.003 Atmosphere, Ocean and Climate Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Contents

### BALANCED FLOW: EXAMPLES (PHH lecture 3) Potential Vorticity in the real atmosphere. Potential temperature θ. Rossby Ertel potential vorticity

BALANCED FLOW: EXAMPLES (PHH lecture 3) Potential Vorticity in the real atmosphere Need to introduce a new measure of the buoyancy Potential temperature θ In a compressible fluid, the relevant measure

### Physical Oceanography, MSCI 3001 Oceanographic Processes, MSCI Dr. Katrin Meissner Week 5.

Physical Oceanography, MSCI 3001 Oceanographic Processes, MSCI 5004 Dr. Katrin Meissner k.meissner@unsw.e.au Week 5 Ocean Dynamics Transport of Volume, Heat & Salt Flux: Amount of heat, salt or volume

### Introduction to Isentropic Coordinates:! a new view of mean meridional & eddy circulations" Cristiana Stan

Introduction to Isentropic Coordinates:! a new view of mean meridional & eddy circulations" Cristiana Stan School and Conference on the General Circulation of the Atmosphere and Oceans: a Modern Perspective!

### Ocean currents: some misconceptions and some dynamics

Ocean currents: some misconceptions and some dynamics Joe LaCasce Dept. Geosciences October 30, 2012 Where is the Gulf Stream? BBC Weather Center Where is the Gulf Stream? Univ. Bergen news website (2011)

### Dynamic Meteorology 1

Dynamic Meteorology 1 Lecture 14 Sahraei Department of Physics, Razi University http://www.razi.ac.ir/sahraei Buys-Ballot rule (Northern Hemisphere) If the wind blows into your back, the Low will be to

### 3. Midlatitude Storm Tracks and the North Atlantic Oscillation

3. Midlatitude Storm Tracks and the North Atlantic Oscillation Copyright 2006 Emily Shuckburgh, University of Cambridge. Not to be quoted or reproduced without permission. EFS 3/1 Review of key results

### 1/25/2010. Circulation and vorticity are the two primary

Lecture 4: Circulation and Vorticity Measurement of Rotation Circulation Bjerknes Circulation Theorem Vorticity Potential Vorticity Conservation of Potential Vorticity Circulation and vorticity are the

### Circulation and Vorticity

Circulation and Vorticity Example: Rotation in the atmosphere water vapor satellite animation Circulation a macroscopic measure of rotation for a finite area of a fluid Vorticity a microscopic measure

### Ocean Circulation- PART- I: In Class. Must be done inclass, and turned in before you leave for credit.

Name: Section/ TA: Ocean Circulation- PART- I: In Class. Must be done inclass, and turned in before you leave for credit. Activity 1: The Sverdrup In our homes, we are used to calculating water volumes

### Chapter 10 Atmospheric Forces & Winds

Chapter 10 Atospheric Forces & Winds Chapter overview: Atospheric Pressure o Horizontal pressure variations o Station vs sea level pressure Winds and weather aps Newton s 2 nd Law Horizontal Forces o Pressure

### 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

### Science 1206 Chapter 1 - Inquiring about Weather

Science 1206 Chapter 1 - Inquiring about Weather 1.1 - The Atmosphere: Energy Transfer and Properties (pp. 10-25) Weather and the Atmosphere weather the physical conditions of the atmosphere at a specific

### EESC V2100 The Climate System spring 2004 Lecture 4: Laws of Atmospheric Motion and Weather

EESC V2100 The Climate System spring 2004 Lecture 4: Laws of Atmospheric Motion and Weather Yochanan Kushnir Lamont Doherty Earth Observatory of Columbia University Palisades, NY 10964, USA kushnir@ldeo.columbia.edu

### ATMO/OPTI 656b Spring 09. Physical properties of the atmosphere

The vertical structure of the atmosphere. Physical properties of the atmosphere To first order, the gas pressure at the bottom of an atmospheric column balances the downward force of gravity on the column.

### Project 2 Fronts

12.307 Project 2 Fronts Lodovica Illari and John Marshall March 2010 Abstract We inspect fronts crossing the country associated with day-to-day variations in the weather using real-time atmospheric observations.

### EATS Notes 1. Some course material will be online at

EATS 3040-2015 Notes 1 14 Aug 2015 Some course material will be online at http://www.yorku.ca/pat/esse3040/ HH = Holton and Hakim. An Introduction to Dynamic Meteorology, 5th Edition. Most of the images

### MAR 110 LECTURE #10 The Oceanic Conveyor Belt Oceanic Thermohaline Circulation

1 MAR 110 LECTURE #10 The Oceanic Conveyor Belt Oceanic Thermohaline Circulation Ocean Climate Temperature Zones The pattern of approximately parallel oceanic surface isotherms (lines of constant temperature)

### 10.1 TEMPERATURE, THERMAL ENERGY AND HEAT Name: Date: Block: (Reference: pp of BC Science 10)

10.1 TEMPERATURE, THERMAL ENERGY AND HEAT Name: Date: Block: (Reference: pp. 424-435 of BC Science 10) kinetic molecular theory: explains that matter is made up of tiny that are constantly. These atoms

### Introduction to Isentropic Coordinates: a new view of mean meridional & eddy circulations. Cristiana Stan

Introduction to Isentropic Coordinates: a new view of mean meridional & eddy circulations Cristiana Stan School and Conference on the General Circulation of the Atmosphere and Oceans: a Modern Perspective

### Chapter 1. Governing Equations of GFD. 1.1 Mass continuity

Chapter 1 Governing Equations of GFD The fluid dynamical governing equations consist of an equation for mass continuity, one for the momentum budget, and one or more additional equations to account for

### The Circulation of the Atmosphere:

The Circulation of the Atmosphere: Laboratory Experiments (see next slide) Fluid held in an annular container is at rest and is subjected to a temperature gradient. The less dense fluid near the warm wall

### 7 Balanced Motion. 7.1 Return of the...scale analysis for hydrostatic balance! CSU ATS601 Fall 2015

7 Balanced Motion We previously discussed the concept of balance earlier, in the context of hydrostatic balance. Recall that the balanced condition means no accelerations (balance of forces). That is,

### Ocean Temperatures. Atlantic Temp Section. Seasonal (Shallow) Thermocline. Better Atlantic Temp Section

I. Fundamental Principles Physical Properties Conservation of Heat Why Does the Ocean Circulate? Waves & Tides Ocean Temperatures II. Ocean Circulation Conservation of Mass Forces & Balance of Forces Effects

### The Planetary Circulation System

12 The Planetary Circulation System Learning Goals After studying this chapter, students should be able to: 1. describe and account for the global patterns of pressure, wind patterns and ocean currents

### Introduction to Physical Oceanography Homework 3 - Solutions. 1. Volume transport in the Gulf Stream and Antarctic Circumpolar current (ACC):

Laure Zanna 10/17/05 Introduction to Physical Oceanography Homework 3 - Solutions 1. Volume transport in the Gulf Stream and Antarctic Circumpolar current (ACC): (a) Looking on the web you can find a lot

### Ocean Mixing and Climate Change

Ocean Mixing and Climate Change Factors inducing seawater mixing Different densities Wind stirring Internal waves breaking Tidal Bottom topography Biogenic Mixing (??) In general, any motion favoring turbulent

### Surface Circulation Ocean current Surface Currents:

All Write Round Robin G1. What makes up the ocean water? G2. What is the source of the salt found in ocean water? G3. How does the water temperature affect the density of ocean water? G4. How does the

### SEVERE AND UNUSUAL WEATHER

SEVERE AND UNUSUAL WEATHER Basic Meteorological Terminology Adiabatic - Referring to a process without the addition or removal of heat. A temperature change may come about as a result of a change in the

### The Transfer of Heat

The Transfer of Heat Outcomes: S2-4-03 Explain effects of heat transfer within the atmosphere and hydrosphere on the development and movement of wind and ocean currents. Coriolis Effect In our ecology

### Transient/Eddy Flux. Transient and Eddy. Flux Components. Lecture 7: Disturbance (Outline) Why transients/eddies matter to zonal and time means?

Lecture 7: Disturbance (Outline) Transients and Eddies Climate Roles Mid-Latitude Cyclones Tropical Hurricanes Mid-Ocean Eddies (From Weather & Climate) Flux Components (1) (2) (3) Three components contribute

### Goals of this Chapter

Waves in the Atmosphere and Oceans Restoring Force Conservation of potential temperature in the presence of positive static stability internal gravity waves Conservation of potential vorticity in the presence

### Temperature. Vertical Thermal Structure. Earth s Climate System. Lecture 1: Introduction to the Climate System

Lecture 1: Introduction to the Climate System T mass (& radiation) T & mass relation in vertical mass (& energy, weather..) Energy T vertical stability vertical motion thunderstorm What are included in

### Lecture #2 Planetary Wave Models. Charles McLandress (Banff Summer School 7-13 May 2005)

Lecture #2 Planetary Wave Models Charles McLandress (Banff Summer School 7-13 May 2005) 1 Outline of Lecture 1. Observational motivation 2. Forced planetary waves in the stratosphere 3. Traveling planetary

### 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,

### ATM 298, Spring 2013 Lecture 2 The Equa;ons of Fluid Mo;on April 3, Paul A. Ullrich (HH 251)

ATM 298, Spring 2013 Lecture 2 The Equa;ons of Fluid Mo;on April 3, 2013 Paul A. Ullrich (HH 251) paullrich@ucdavis.edu Global Atmospheric Modeling Global atmospheric models were originally constructed

### 2/15/2012. Earth System Science II EES 717 Spring 2012

Earth System Science II EES 717 Spring 2012 1. The Earth Interior Mantle Convection & Plate Tectonics 2. The Atmosphere - Climate Models, Climate Change and Feedback Processes 3. The Oceans Circulation;

### GFD 2 Spring 2010 P.B. Rhines Problem set 1-solns out: 5 April back: 12 April

GFD 2 Spring 2010 P.B. Rhines Problem set 1-solns out: 5 April back: 12 April 1 The Gulf Stream has a dramatic thermal-wind signature : the sloping isotherms and isohalines (hence isopycnals) not only

### Why Is the Mountain Peak Cold? Lecture 7: Air cools when it rises. Vertical Thermal Structure. Three Things Need To Be Explained

Lecture 7: Air cools when it rises Air expands as it rises Air cools as it expands Air pressure Lapse rates Why Is the Mountain Peak Cold? Sunlight heats the atmosphere from below Convection occurs and

### Lecture 14. Equations of Motion Currents With Friction Sverdrup, Stommel, and Munk Solutions Remember that Ekman's solution for wind-induced transport

Lecture 14. Equations of Motion Currents With Friction Sverdrup, Stommel, and Munk Solutions Remember that Ekman's solution for wind-induced transport is which can also be written as (14.1) i.e., #Q x,y