# ESCI 343 Atmospheric Dynamics II Lesson 10 - Topographic Waves

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 ESCI 343 Atmospheric Dynamics II Lesson 10 - Topographic Waves Reference: An Introduction to Dynamic Meteorology (3 rd edition), J.R. Holton Reading: Holton, Section 7.4. STATIONARY WAVES Waves will appear to be stationary if their phase speed is equal and opposite to the mean flow, c = u. (1) Stationary waves will have a frequency of zero, since they do not oscillate in time, only in space. For dispersive waves, the wavelength of the stationary wave will correspond to that wavelength which has a phase speed equal and opposite to the mean flow. None of the other wavelengths will be stationary. An example of stationary waves is the stationary wave pattern that forms in a river when it flows over a submerged rock or obstacle. The flow of the obstacle generates many different waves of various wavelengths, but only the ones whose phase speed is equal and opposite to the flow will remain stationary. If the flow speeds up or slows down, the wavelength of the stationary wave will change. DISPERSION RELATION FOR STATIONARY INTERNAL GRAVITY WAVES In the atmosphere, flow of a stably stratified fluid over a mountain barrier can also generate standing waves. If we consider the flow over a sinusoidal pattern of ridges that are perpendicular with the x-axis, and with a horizontal wave number of k, then we can analyze the structure of these waves. Since these waves are internal gravity waves in the presence of a mean flow their phase speed and dispersion relation is simply N c = u ± () kn ω = uk ± (remember that since these are linear waves, the mean flow simply adds a term u k to the frequency). But, we are only interested in the standing waves generated by the topography, for which the phase speed (and therefore, frequency) is zero. For standing waves then, we have N u ± = 0. (3) The horizontal wave number, k, is determined by the wave number of the terrain; u and N are properties of the atmosphere. Since these quantities are predetermined, then there is only one value of vertical wave number, m, which can satisfy the dispersion relation. Thus, m is given by N m = k. (4) u Equation (4) is the dispersion relation for stationary internal gravity waves.

2 VERTICALLY PROPAGATING VERSUS VERTICALLY DECAYING WAVES The vertical structure of the standing waves is determined by how N, k, and u relate to one another. Vertically propagating waves. If k < N u then the right hand side is positive, and m is real. This corresponds to waves that propagate vertically, since the sinusoidal form for the dependent variables is i( kx+ mz ) e. (5) Along lines of constant phase (kx + mz) the following relation holds kx + mz = b (6) where b is a constant. This means that phase lines obey the following equation, k b z = x +. m m (7) This tells us that the lines of constant phase tilt upwind with height, since they have a negative slope (see figure below). Since the wave is propagating upstream (it has to be, since it is a standing wave), the individual wave crests have a downward component of phase speed. This means that the group velocity is upward, so that topographically forced waves propagate energy upward. Vertically propagating topographically-forced stationary waves. The wind speed is from left-to-right. This is for u < N k, so the value of m is positive and m is real. Solid lines are streamfunction; colors are for vertical velocity. Vertically decaying waves. If k > N u then the right-hand-side negative. In this case the sinusoidal form for the dependent variables is mz e ikx e,

3 and the waves decay with height (such waves are also known as evanescent).. In this case, lines of constant phase are vertical. This is illustrated in the figure below. Vertically decaying topographically-forced stationary waves. This is for u > N k, so the value of m is negative and m is imaginary. Solid lines are streamfunction; colors are for vertical velocity. WAVES GENERATED BY AN ISOLATED MOUNTAIN RIDGE In the real world, mountains are not pure sinusoids. However, through Fourier analysis, we can approximate the real topography by its Fourier components,, with the component of wave number k having an amplitude of H(k). H(k) and h(x) are the Fourier transforms of each other, and are defined by the following equations h( x) = H ( k) = H ( k) e 1 π ikx h( x) e dk ikx dx (8) A very sharp, or discontinuous function has a greater number of high frequency (high wave number) components inn its transform. A broad function has few high frequency components, and is mostly made up of low frequency (low wave number) components. Flow over a mountainn will generate a whole spectrum of gravity waves. Each wave component generated will either propagate vertically, or decay vertically, depending on whether its vertical wave number (m) determined from N m = k (9) u is real or imaginary. Based on the previous discussion of Fourier transforms, we expect that a narrow mountain will generate a lot of high wave number gravity waves, while a broad mountain will generatee more low wave-number gravity waves. 3

4 Whether or not flow over an isolated mountain will generate vertically propagating waves, or vertically decaying waves, depends on the wind speed and the width of the mountain. Vertically propagating waves are more likely if the wind speed is slow, or the mountain is wide. Faster wind speeds and narrower mountains are more likely to result in vertically decaying waves. The plots below are for various wind speeds over a Gaussian-shaped hill. The wind speed in each plot is constant, but is faster in each successive plot. TRAPPED (LEE) WAVES In the previous discussion on mountain waves, we ve assumed that the mean flow does not have vertical shear, and that the static stability is constant with height. Since wind speed normally increases with height it is possible that (9) will yield vertically propagating waves in the lower layer, but have vertically decaying waves in the upper part of the atmosphere. This is illustrated in the figure below. In this figure there are two distinct vertical layers. In each layer the quantity N u (called the Scorer parameter) is constant (though N and u themselves may vary within each layer). If the upper layer has a larger wind speed and/or lower stability, then the scorer parameter is largerr in the lower layer than in the upper layer. This results in waves that are trapped in the lower layer downwind of the mountain. 4

5 EXERCISES 1. For an isothermal, compressible atmosphere show the following (remember that H = R T g ): a. = γ gh c s 1 b. N = ( g H )( 1 γ ). Assume that the Allegheny Mountains can be approximated as a parallel series of ridges approximately 5 km apart. Also, assume an isothermal, compressible atmosphere with a scale height of 8100 m. Calculate the critical wind speed below which topographically forced waves will propagate vertically, and above which they will decay with height. 5

### Downslope Wind Storms

Downslope Wind Storms How does acceleration over the wing affect pressure field? Equation of Motion for frictionless flow: V t = l k α p+g If we assume a horizontally homogeneous, hydrostatic reference

### A new theory for downslope windstorms and trapped lee wave François Lott Lab. Météorologie Dynamique, Ecole Normale Supérieure, Paris

A new theory for downslope windstorms and trapped lee wave François Lott Lab. Météorologie Dynamique, Ecole Normale Supérieure, Paris 1)Motivation: trapped lee waves 2)Model description 3)Downslope windstorms

### Chapter 11 Waves. Waves transport energy without transporting matter. The intensity is the average power per unit area. It is measured in W/m 2.

Chapter 11 Waves Energy can be transported by particles or waves A wave is characterized as some sort of disturbance that travels away from a source. The key difference between particles and waves is a

### Waves Part II. non-dispersive (C g =C)

Waves Part II Previously we discussed Surface Gravity Waves Deep Water Waves Shallow Water Waves C g T 2 C g h dispersive (C g =C/2) Definitions: phase speed C= /T= /k non-dispersive (C g =C) group speed

### Gravity waves and bores. Material kindly provided by Dr. Steven Koch GSD NOAA (Boulder, CO)

Gravity waves and bores Material kindly provided by Dr. Steven Koch GSD NOAA (Boulder, CO) Presented at Iowa State University 11 April 2005 What is a gravity wave? An oscillation caused by the displacement

### Similarly to elastic waves, sound and other propagated waves are graphically shown by the graph:

Phys 300/301 Physics: Algebra/Trig Eugene Hecht, 3e. Prepared 01/24/06 11.0 Waves & Sounds There are two fundamental waves of transporting energy and momentum: particles and waves. While they seem opposites,

### Impact of non hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

Impact of non hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow Article Accepted Version Yu, C. L. and Teixeira, M. A. C. (25) Impact of nonhydrostatic effects

### 4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES Student Notes

4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES Student Notes I. DIFFERENT TYPES OF WAVES A. TRANSVERSE AND LONGITUDINAL WAVES B. WAVE PULSES AND TRAVELLING WAVES C. SOUND AND WATER WAVES II. DEFINING TERMS

### Movement and Position

Movement and Position Syllabus points: 1.2 plot and interpret distance-time graphs 1.3 know and use the relationship between average speed, distance moved and 1.4 describe experiments to investigate the

### Chapter 14. Vibrations and Waves

Chapter 14 Vibrations and Waves Chapter 14 Vibrations and Waves In this chapter you will: Examine vibrational motion and learn how it relates to waves. Determine how waves transfer energy. Describe wave

### LECTURE OUTLINE CHAPTER 14

1 LECTURE OUTLINE CHAPTER 14 Waves and Sound 14-1 Types of Waves 2 A wave: Is a disturbance that propagates from one place to another. 1- Transverse Wave: The displacement of the medium is perpendicular

### Mechanical Waves. Chapter 15. PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman

Chapter 15 Mechanical Waves PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 15 To study the properties and

### 2.4. Applications of Boundary Layer Meteorology

2.4. Applications of Boundary Layer Meteorology 2.4.1. Temporal Evolution & Prediction of the PBL Earlier, we saw the following figure showing the diurnal evolution of PBL. With a typical diurnal cycle,

### 1. A tendency to roll or heel when turning (a known and typically constant disturbance) 2. Motion induced by surface waves of certain frequencies.

Department of Mechanical Engineering Massachusetts Institute of Technology 2.14 Analysis and Design of Feedback Control Systems Fall 2004 October 21, 2004 Case Study on Ship Roll Control Problem Statement:

### The impacts of explicitly simulated gravity waves on large-scale circulation in the

The impacts of explicitly simulated gravity waves on large-scale circulation in the Southern Hemisphere. Linda Mudoni Department of Geological and Atmospheric Sciences October 2003 Introduction In the

### 4-3 Rate of Change and Slope. Warm Up. 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2.

Warm Up 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2. Objectives Find rates of change and slopes. Relate a constant rate of change to the slope of

### What Do You Think? GOALS

Activity 3 Slinkies and Waves GOALS In this activity you will: Make a people wave. Generate longitudinal and transverse waves on a Slinky. Label the parts of a wave. Analyze the behavior of waves on a

### WAVES. Pulses are disturbances or a single wave motion. A continuous production of pulses will give rise to a progressive wave (wave train).

1 WAVES Types of Waves Pulses Pulses are disturbances or a single wave motion. A continuous production of pulses will give rise to a progressive wave (wave train). Progressive Waves A progressive wave

### Chapter 12: Mechanical Waves and Sound

Chapter 12 Lecture Chapter 12: Mechanical Waves and Sound Goals for Chapter 12 To describe mechanical waves. To study superposition, standing waves and sound. To present sound as a standing longitudinal

### Chapter 10 Waves. wave energy NOT the water particles moves across the surface of the sea. wave form moves and with it, energy is transmitted

Capillary Waves, Wind Waves, Chapter 10 Waves Anatomy of a Wave more like a real wave Tsunamis, Internal waves big waves huge waves rogue waves small waves more like a sine wave Wave direction Wave wave

### Mesoscale Atmospheric Systems. Upper-level fronts. 13 and 20 March 2018 Heini Wernli. 13 March 2018 H. Wernli 1

Mesoscale Atmospheric Systems Upper-level fronts 13 and 20 March 2018 Heini Wernli 13 March 2018 H. Wernli 1 Upper-level fronts Formation of fronts is favored by presence of quasi-horizontal boundaries:

### ESCI 485 Air/sea Interaction Lesson 9 Equatorial Adjustment and El Nino Dr. DeCaria

ESCI 485 Air/sea Interaction Lesson 9 Equatorial Adjustment and El Nino Dr. DeCaria Reference: El Nino, La Nina, and the Southern Oscillation, Philander THE TWO-LAYER SHALLOW WATER MODEL The ocean can

### DETRMINATION OF A PLUNGER TYPE WAVE MAKER CHARACTERISTICE IN A TOWING TANK

The 9 th International Conference on Coasts, Ports and Marine Structures (ICOPMAS 2010) 29 Nov.-1 Dec. 2010 (Tehran) DETRMINATION OF A PLUNGER TYPE WAVE MAKER CHARACTERISTICE IN A TOWING TANK sayed mohammad

### Upstream-Propagating Wave Modes in Moist and Dry Flow over Topography

3060 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 69 Upstream-Propagating Wave Modes in Moist and Dry Flow over Topography TEDDIE L. KELLER, RICHARD ROTUNNO, MATTHIAS STEINER, AND

### DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 11-7: WAVE MOTION LSN 11-8: TYPES OF WAVES; LONGITUDINAL AND TRANSVERSE LSN 11-9: ENERGY TRANSPORTED BY WAVES Physics of Waves Questions From Reading

### Physics 1C. Lecture 12C. "Fluctuat nec mergitur. = She is swayed by the waves but does not sink." --Motto of the city of Paris

Physics 1C Lecture 12C "Fluctuat nec mergitur. = She is swayed by the waves but does not sink." --Motto of the city of Paris Outline Homework is intended for practice and preparation It is the basis for

### Chapter 3 PRESSURE AND FLUID STATICS

Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 3 PRESSURE AND FLUID STATICS Lecture slides by Hasan Hacışevki Copyright The McGraw-Hill

### Modelling and Simulation of Environmental Disturbances

Modelling and Simulation of Environmental Disturbances (Module 5) Dr Tristan Perez Centre for Complex Dynamic Systems and Control (CDSC) Prof. Thor I Fossen Department of Engineering Cybernetics 18/09/2007

### Sea and Land Breezes METR 4433, Mesoscale Meteorology Spring 2006 (some of the material in this section came from ZMAG)

Sea and Land Breezes METR 4433, Mesoscale Meteorology Spring 2006 (some of the material in this section came from ZMAG) 1 Definitions: The sea breeze is a local, thermally direct circulation arising from

### Standard atmosphere Typical height (m) Pressure (mb)

Standard atmosphere Pressure (mb) Typical height (ft) Typical height (m) 1013.25 0 0 1000 370 110 850 4780 1460 700 9880 3010 500 18280 5570 300 30050 9160 Whiteman 2000 Pressure decreases exponentially

### Physics 2048 Test 1 Fall 2000 Dr. Jeff Saul Name:

Physics 2048 Test 1 Fall 2000 Dr. Jeff Saul Name: READ THESE INSTRUCTIONS BEFORE YOU BEGIN Before you start the test, WRITE YOUR NAME ON EVERY PAGE OF THE EXAM. Calculators are permitted, but no notes

### An Atlas of Oceanic Internal Solitary Waves (February 2004) by Global Ocean Associates Prepared for Office of Naval Research Code 322 PO

Overview The is located in the North Atlantic Ocean between southern Ireland and southwest England (Figure 1). The Sea s western edge covers a continental shelf region characterized by rough and irregular

### Physics 1-2 Mr. Chumbley Physics: Chapter 11 p

Physics 1-2 Mr. Chumbley Physics: Chapter 11 p. 362-401 Section 1 p. 364 371 Section 2 p. 372-377 Simple Harmonic Motion There exist many different situations in which objects oscillate in regular, repeating

### Lesson 48: Wave Velocity and Boundaries

Lesson 48: Wave Velocity and Boundaries Wave Velocity The speed of a wave does not depend on the amplitude or wavelength of the wave. Instead, the speed of the wave is determined by the properties of the

### Oceans in Motion: Waves and Tides

Oceans in Motion: Waves and Tides Waves Waves are among the most familiar features in the ocean. All waves work similarly, so although we are talking about ocean waves here, the same information would

### Fluid Mechanics HYDRO STATICS

Fluid Mechanics HYDRO STATICS Fluid Mechanics STABILITY OF FLOATING BODIES Any floating body is subjected by two opposing vertical forces. One is the body's weight W which is downward, and the other is

### Section 1 Types of Waves. Distinguish between mechanical waves and electromagnetic waves.

Section 1 Types of Waves Objectives Recognize that waves transfer energy. Distinguish between mechanical waves and electromagnetic waves. Explain the relationship between particle vibration and wave motion.

### Sound scattering by hydrodynamic wakes of sea animals

ICES Journal of Marine Science, 53: 377 381. 1996 Sound scattering by hydrodynamic wakes of sea animals Dmitry A. Selivanovsky and Alexander B. Ezersky Selivanovsky, D. A. and Ezersky, A. B. 1996. Sound

### DRAFT OMAE REAL TIME WAVE FORECASTING FOR REAL TIME SHIP MOTION PREDICTIONS

Proceedings of the 7 th International Conference on Offshore echanics and Arctic Engineering OAE June 5-, 8, Estoril, Portugal DRAFT OAE8-5784 REAL TIE WAVE FORECASTING FOR REAL TIE SHIP OTION PREDICTIONS

### BUOYANCY, FLOATATION AND STABILITY

BUOYANCY, FLOATATION AND STABILITY Archimedes Principle When a stationary body is completely submerged in a fluid, or floating so that it is only partially submerged, the resultant fluid force acting on

### A It is halved. B It is doubled. C It is quadrupled. D It remains the same.

WAVES UNIT REVIEW EN: CALIFORNIA STATE QUESTIONS: 1. A sound wave is produced in a metal cylinder by striking one end. Which of the following occurs as the wave travels along the cylinder? A Its amplitude

### Defined as a transfer of energy, in the form of a temporary disturbance of a medium, where the medium itself does not move.

Waves: Defined as a transfer of energy, in the form of a temporary disturbance of a medium, where the medium itself does not move. Three Classifications of waves: 1. Mechanical waves: These are waves that

### time v (vertical) time

NT4E-QRT20: PROJECTILE MOTION FOR TWO ROCKS VELOCITY AND ACCELERATION GRAPHS II Two identical rocks are thrown horizontally from a cliff with Rock A having a greater velocity at the instant it is released

### Lecture Outline Chapter 15. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 15 Physics, 4 th Edition James S. Walker Chapter 15 Fluids Density Units of Chapter 15 Pressure Static Equilibrium in Fluids: Pressure and Depth Archimedes Principle and Buoyancy

### Lecture Outline Chapter 14. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 14 Physics, 4 th Edition James S. Walker Chapter 14 Waves and Sound Units of Chapter 14 Types of Waves Waves on a String Harmonic Wave Functions Sound Waves Sound Intensity The

### CHAPTER 10: LINEAR KINEMATICS OF HUMAN MOVEMENT

CHAPTER 10: LINEAR KINEMATICS OF HUMAN MOVEMENT 1. Vector mechanics apply to which of the following? A. displacement B. velocity C. speed D. both displacement and velocity 2. If velocity is constant, then

### Validation of Measurements from a ZephIR Lidar

Validation of Measurements from a ZephIR Lidar Peter Argyle, Simon Watson CREST, Loughborough University, Loughborough, United Kingdom p.argyle@lboro.ac.uk INTRODUCTION Wind farm construction projects

### An Undular Bore and Gravity Waves Illustrated by Dramatic Time-Lapse Photography

AUGUST 2010 C O L E M A N E T A L. 1355 An Undular Bore and Gravity Waves Illustrated by Dramatic Time-Lapse Photography TIMOTHY A. COLEMAN AND KEVIN R. KNUPP Department of Atmospheric Science, University

### Exercises Vibration of a Pendulum (page 491) 25.2 Wave Description (pages ) 25.3 Wave Motion (pages )

Exercises 25.1 Vibration of a Pendulum (page 491) 1. The time it takes for one back-and-forth motion of a pendulum is called the. 2. List the two things that determine the period of a pendulum. 3. Circle

### Section 1 Types of Waves

CHAPTER OUTLINE Section 1 Types of Waves Key Idea questions > What does a wave carry? > How are waves generated? > What is the difference between a transverse wave and a longitudinal wave? > How do the

### Principles of Sailing

Principles of Sailing This is a PowerPoint set of charts presented by Demetri Telionis on March 21, 2015 at the Yacht Club of Hilton Head Island. The aim of this presentation was to help the audience understand

### Patchy mixing in the Indian Ocean

CPT: Representing internal-wave driven mixing in global ocean models The Team: Matthew Alford (UW) Brian Arbic (U Michigan) Frank Bryan (NCAR) Eric Chassignet (FSU) Gokhan Danabasoglu (NCAR) Peter Gent

### WAVE LOAD ACTING ON HORIZONTAL PLATE DUE TO BORE

Proceedings of the 6 th International Conference on the Application of Physical Modelling in Coastal and Port Engineering and Science (Coastlab16) Ottawa, Canada, May 10-13, 2016 Copyright : Creative Commons

### Ocean Wave Forecasting

Ocean Wave Forecasting Jean-Raymond Bidlot* Marine Prediction Section Predictability Division of the Research Department European Centre for Medium-range Weather Forecasts (E.C.M.W.F.) Reading, UK * With

### Review packet Physical Science Unit Waves - 1

Review packet Physical Science Unit Waves - 1 1. A stretched spring attached to two fixed points is compressed on one end and released, as shown below. 4. When the density of a substance is measured, which

### Waves-Wave Basics. 1. Which type of wave requires a material medium through which to travel? 1. sound 2. television 3. radio 4.

1. Which type of wave requires a material medium through which to travel? 1. sound 2. television 3. radio 4. x ray 2. A single vibratory disturbance moving through a medium is called 1. a node 2. an antinode

### THE POLARIMETRIC CHARACTERISTICS OF BOTTOM TOPOGRAPHY RELATED FEATURES ON SAR IMAGES

THE POLARIMETRIC CHARACTERISTICS OF BOTTOM TOPOGRAPHY RELATED FEATURES ON SAR IMAGES Taerim Kim Professor, Ocean System Eng. Dept. Kunsan University Miryong Dong San 68, Kunsan, Jeonbuk, Korea, trkim@kunsan.ac.kr

### A Little Math. Wave speed = wave length/wave period C= L/T. Relationship of Wave Length to Depth of Wave Motion

Ocean Waves 1 2 1 A Little Math Wave speed = wave length/wave period C= L/T 3 Relationship of Wave Length to Depth of Wave Motion 4 2 Motion of Water as Wave Passes Water in the crest of the wave move

### Applications of Bernoulli s principle. Principle states that areas with faster moving fluids will experience less pressure

Applications of Bernoulli s principle Principle states that areas with faster moving fluids will experience less pressure Artery o When blood flows through narrower regions of arteries, the speed increases

### HITES, 2011 Lecture 1 1. You are in a boat out on the ocean watching the waves go by. To fully describe the waves, you need three things:

Waves A wave is a that propagates p in a certain direction with a certain speed. 1D 2D 3D Physical medium Waves in water Waves in elastic bodies Sound Empty space (a vacuum) Electromagnetic waves HITES,

Pressure Variation with Depth Pressure in a static fluid does not change in the horizontal direction as the horizontal forces balance each other out. However, pressure in a static fluid does change with

### Ball Toss. Vernier Motion Detector

Experiment 6 When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time would

### Chapter 10 Lecture Outline. The Restless Oceans

Chapter 10 Lecture Outline The Restless Oceans Focus Question 10.1 How does the Coriolis effect influence ocean currents? The Ocean s Surface Circulation Ocean currents Masses of water that flow from one

### Walk - Run Activity --An S and P Wave Travel Time Simulation ( S minus P Earthquake Location Method)

Walk - Run Activity --An S and P Wave Travel Time Simulation ( S minus P Earthquake Location Method) L. W. Braile and S. J. Braile (June, 2000) braile@purdue.edu http://web.ics.purdue.edu/~braile Walk

### 19 Waves and Vibrations

19 Waves and Vibrations Answers and Solutions for Chapter 19 Reading Check Questions 1. A wiggle in time is a vibration; a wiggle in space and time is a wave. 2. The source of all waves is a vibration.

### Agood tennis player knows instinctively how hard to hit a ball and at what angle to get the ball over the. Ball Trajectories

42 Ball Trajectories Factors Influencing the Flight of the Ball Nathalie Tauziat, France By Rod Cross Introduction Agood tennis player knows instinctively how hard to hit a ball and at what angle to get

### An Atlas of Oceanic Internal Solitary Waves (May 2002) by Global Ocean Associates Prepared for the Office of Naval Research - Code 322PO

Overview is located in the western Pacific Ocean along the west side of the Philippines (between approximately 5 o and 11 o N. latitude and 117 o and 123 o E. longitude). It is a deepwater sea, roughly

### Air Pollution Dispersion

Air Pollution Dispersion Dispersion Processes Convective Dispersion Air Parcel Dynamics Adiabatic Process Lapse Rate Equilibrium and Stability Atmospheric Stability Stability and Dispersion Temperature

### Effect of channel slope on flow characteristics of undular hydraulic jumps

River Basin Management III 33 Effect of channel slope on flow characteristics of undular hydraulic jumps H. Gotoh, Y. Yasuda & I. Ohtsu Department of Civil Engineering, College of Science and Technology,

### ATMS 310 Tropical Dynamics

ATMS 310 Tropical Dynamics Introduction Throughout the semester we have focused on mid-latitude dynamics. This is not to say that the dynamics of other parts of the world, such as the tropics, are any

### Outline. Wind Turbine Siting. Roughness. Wind Farm Design 4/7/2015

Wind Turbine Siting Andrew Kusiak 2139 Seamans Center Iowa City, Iowa 52242-1527 andrew-kusiak@uiowa.edu Tel: 319-335-5934 Fax: 319-335-5669 http://www.icaen.uiowa.edu/~ankusiak Terrain roughness Escarpments

### 1. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?

Chapter Problems Motion at Constant Speed Class Work. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?. During the first 50 s a truck traveled at constant speed of 5 m/s.

### LOW PRESSURE EFFUSION OF GASES revised by Igor Bolotin 03/05/12

LOW PRESSURE EFFUSION OF GASES revised by Igor Bolotin 03/05/ This experiment will introduce you to the kinetic properties of low-pressure gases. You will make observations on the rates with which selected

### Introduction to Waves and Sound

Introduction to Waves and Sound Principal Authors: Martin Mason, Mt. San Antonio College and Christine Carmichael, Woodbury University Based on the work of John Terrell and Roger Edmonds, Middlesex Community

### Chapter. The Dynamic Ocean

Chapter The Dynamic Ocean An ocean current is the mass of ocean water that flows from one place to another. 16.1 The Composition of Seawater Surface Circulation Surface Currents Surface currents are movements

### MECHANICAL WAVES AND SOUND

MECHANICAL WAVES AND SOUND Waves Substances have a stable equilibrium state Uniform pressure everywhere throughout the substance Atomic springs are at their equilibrium length Can make a wave by disturbing

### Lesson: Ocean Circulation

Lesson: Ocean Circulation By Keith Meldahl Corresponding to Chapter 9: Ocean Circulation As this figure shows, there is a connection between the prevailing easterly and westerly winds (discussed in Chapter

### Determination of the wind pressure distribution on the facade of the triangularly shaped high-rise building structure

Determination of the wind pressure distribution on the facade of the triangularly shaped high-rise building structure Norbert Jendzelovsky 1,*, Roland Antal 1 and Lenka Konecna 1 1 STU in Bratislava, Faculty

### The Estimation of Ship Velocity from a SAR Image

The Estimation of Ship Velocity from a SAR Image James K.E. Tunaley, Radar Applications and Space Technology Section DRDC Ottawa Defence R&D Canada R et D pour la défense Canada Canada OBJECTIVES Ship

### In the liquid phase, molecules can flow freely from position. another. A liquid takes the shape of its container. 19.

In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container. In the liquid phase, molecules can flow freely from position

### g) Use the map compass to provide the general locality of the knoll on the chart.

The horizontal scale (x axis) of your cross-section/profile is the linear map distance between point A and point B on the map (or between X and Y and Z). It conforms to the map scale. In other words, the

### EDEXCEL NATIONALS UNIT 6 MECHANICAL PRINCIPLES and APPLICATIONS. ASSIGNMENT No. 4

EDEXCEL NATIONALS UNIT 6 MECHANICAL PRINCIPLES and APPLICATIONS ASSIGNMENT No. 4 NAME: I agree to the assessment as contained in this assignment. I confirm that the work submitted is my own work. Signature

### In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container.

In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container. In the liquid phase, molecules can flow freely from position

### Undertow - Zonation of Flow in Broken Wave Bores

Nearshore Circulation Undertow and Rip Cells Undertow - Zonation of Flow in Broken Wave Bores In the wave breaking process, the landward transfer of water, associated with bore and surface roller decay

### The physicist's greatest tool is his wastebasket Albert Einstein

Chapter 20: Waves The physicist's greatest tool is his wastebasket Albert Einstein 2 20.1 Waves Describe transverse and longitudinal waves. Learn the properties of waves. Calculate the speed of a wave.

### LOW PRESSURE EFFUSION OF GASES adapted by Luke Hanley and Mike Trenary

ADH 1/7/014 LOW PRESSURE EFFUSION OF GASES adapted by Luke Hanley and Mike Trenary This experiment will introduce you to the kinetic properties of low-pressure gases. You will make observations on the

### U S F O S B u o y a n c y And Hydrodynamic M a s s

1 U S F O S B u o y a n c y And Hydrodynamic M a s s 2 CONTENTS: 1 INTRODUCTION... 3 2 ACCURACY LEVELS... 3 2.1 LEVEL-0... 3 2.2 LEVEL-1... 3 2.3 PANEL MODEL... 3 3 EX 1. SINGLE PIPE. NON FLOODED... 4

### PRE-TEST Module 2 The Principles of Flight Units /60 points

PRE-TEST Module 2 The Principles of Flight Units 1-2-3.../60 points 1 Answer the following questions. (20 p.) moving the plane (4) upward / forward. Opposed to that is 1. What are the names of the four

### CHAPTER 10 WAVES. Section 10.1 Types of Waves

CHAPTER 10 WAVES Section 10.1 Types of Waves What does a wave carry? How are waves generated? What is the difference between a transverse wave and a longitudinal waves? How do the particles in ocean waves

### Chapter 11 Tides. A tidal bore is formed when a tide arrives to an enclosed river mouth. This is a forced wave that breaks.

Chapter 11 Tides A tidal bore is formed when a tide arrives to an enclosed river mouth. This is a forced wave that breaks. Tidal range can be very large Tide - rhythmic oscillation of the ocean surface

### Chapter 2: Pure Substances a) Phase Change, Property Tables and Diagrams

Chapter 2: Pure Substances a) Phase Change, Property Tables and Diagrams In this chapter we consider the property values and relationships of a pure substance (such as water) which can exist in three phases

### SINGULAR WAVES, PROPAGATION AND PROGNOSIS. H. Günther, W. Rosenthal

SINGULAR WAVES, PROPAGATION AND PROGNOSIS H. Günther, W. Rosenthal GKSS Research Center Geesthacht Institute for Coastal Research Geesthacht, Germany Within the last years a high number of large ships

### Effects of an Inclined Land Surface on the Land and Sea Breeze Circulation: A Numerical Experiment. By Tomb Asai

December 1978 T. Asai and S. Mitsumoto 559 Effects of an Inclined Land Surface on the Land and Sea Breeze Circulation: A Numerical Experiment By Tomb Asai Ocean Research Institute, University of Tokyo

### Bernoulli's Principle

Bernoulli's Principle Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases. Introduction The Bernoulli's Principle explains the behavior of

### Atmospheric Stability/Skew-T Diagrams. Fall 2016

Atmospheric Stability/Skew-T Diagrams Fall 2016 Air Parcel Consider a parcel of infinitesimal dimensions that is: Thermally isolated from the environment so that its temperature changes adiabatically as

### Parametric Ball Toss TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Math Objectives Students will be able to use parametric equations to represent the height of a ball as a function of time as well as the path of a ball that has been thrown straight up. Students will be

### Mechanical Waves. Mechanical waves are created by the vibration of objects. Mechanical waves can be either transverse or longitudinal.

Mechanical Waves Mechanical waves are created by the vibration of objects. Mechanical waves can be either transverse or longitudinal. When an object vibrates, its vibrations form mechanical waves that