Turbulent Mean Flow Effects: Inclusion of Rotation
|
|
- Myron Short
- 5 years ago
- Views:
Transcription
1 Turbulent Mean Flow Effects: Inclusion of Rotation Ocean Edd L U H Horizontal Equation of Motion Du 1 1 f u h p Dt z where D u u u ' w' kz Dt t z Added horizontal Friction (eddies) u u 1 v u u p u u u ( ) ( ) t z z i i i i i i i u w f u i kz A h i
2 Road to Geostroph: Diensional Analsis Acceleration Advection Coriolis Pressure Gradient Vertical Friction Horizontal Friction u u 1 v u u p u u u ( ) ( ) t z z i i i i i i i u w f u i kz A h 0 i U U U WU U ku z AU h = = fu? T L L H L H L U Ro fl Rossb Nuber Divide b fu If Ro 1, Ez 1, Eh 1 1 p Geostroph ( f u) i E 1? z fh i k A fl z h Eh Vertical EkanNuber Horizontal Ekan Nuber
3 Large Scale (Non Turbulent) Oceanic Characteristic Scales Open Ocean L U H L ~ sec 3 H ~ 10 f 10 sec U ~ 10 k= A=10-10 U Ro fl E E z h k fh = =(10 10 ) A fl -3-7 (10 10 ) sec sec Coastal Ocean L U H L ~ sec 1 H ~ 10 f 10 sec U ~ 10 k= A=10-10 U Ro fl E E z h k fh = =(10 10 ) A fl -1-3 (10 10 ) sec sec
4 Geostroph Northern Latitude
5 z z=d z=0 Geostrophic Equations p p p = fv = g z = B fu Barotropic Flow 0 v p A p B A >0 D-z p Hdrostatic Equation p = g( D p = g 1 p g v = f f 0 direction Flow into screen Flow out screen z
6 Eaple: The sea surface of a certain arginal sea of unifor densit and depth of 150 slopes to the north with a change in sea surface height of 1 c ever 10 k. Assue that it is in the northern heisphere. If the latitude of this sea is such that the Coriolis frequenc is given b f = 10-4 sec -1 (a) what is the agnitude and direction of the current at the surface, z =0? (b) at id depth, z =75? Eplain in words how our answer to (a) and (b) would change if this sea were located at a latitude lower and latitude higher than assued above. Assue the sae sea surface height and depth for this part. 10 k 1 c Z =75 North
7 z =0 10 k 1 c Z =75 North g v sec.1 f 4 10 sec
8 Ekan Dnaics
9 Ekan Dnaics Du 1 p 1 fv ( )+ Dt z Dv 1 p 1 fu ( ) Dt z fu Eaple A: Stead state, no pressure gradient, wind blows in direction, constant densit Y { } s q Y udz, where Y is length over which the stress occurs. f D z Note : D is defined b { } 0 0 q Volue Transport M q ass or Ekan transport zd 0
10 Ekan Transport { } s Ekan Laer q q Volue Transport Y udz Y f { } 0 s Y Y u X = ( *) f Note: X,Y are the characteristic lengths over which the wind stress occurs and transport occur.
11 Coastal Upwelling X Wind D Ekan Laer q w upwelling q X u w z w u ( q) ( u*) dz XY Xf
12 U 10 Upwelling Eaple Wind ( ) blows to the south off of Northern California just north of Montere Ba (latitude 37 o N) at stead rate of 10 /sec. If the coastal region being affected has diensions, X = 0 k, Y = 50 k, as shown in the figure below, estiate : (a) the Ekan volue transport, q, (b) upwelling velocit, w, and (c) how long it would take nutrients located at a depth of 100 to rise to the surface. q 100 Note: f * sin( *sin(37* ) sec sec kg (10 ) ( u*) sec.510 ( ) kg water water 1000 sec aircu D 10 4
13 Upwelling Eaple Continued q Y (a) q = ( u*) =.510 ( ) Sv 5 1 f sec sec sec ( ) q ( u*) sec 4 ( b) w =1 XY Xf sec sec da H 100 ( c) t 8 das w 1 da Sv 10 sec
14 Ekan Dnaics: Upper Ocean Current Field (Assuptions: stead state, no surface slope, p=0, infinitel deep water, constant densit ) 1 fv z 1 fu z Edd Viscosit Assuption u k z v k z Surface Boundar Condition u s k z=0 = (u*) z Specif Direction of s 0 1 z b Note: z z f b k -1 Note: b is the "effective" Ekan depth where bh u e U U (Deep water assuption)
15 Solution for { ( z)} = 0 { ( z)} = z0 z0 s s u U ep[ bz]cos( bz v U ep[ bz]sin( bz ( u*) U fk fk Note: z negative downward 45 o u Solution for { ( z)} = { ( z)} = 0 u U ep[ bz]sin( bz v U ep[ bz]cos( bz ( u*) U fk fk z0 s z0 Note: z negative downward 45 o s u
16 o Eaple: At a latitude of 45 N wind, U10,blows to the north at 10 /sec. - Observations show that the edd viscosit is. k =10 sec (a) What is the effective Ekan depth? (b) What is the agnitude and direction of the surface stress and surface current at z 0? ( c ) What is the agnitude and direction of the current and stress at z 5, 0. (d) Estiate the turbulent velocit at z 0, 5, 0. (e) How deep would ou have to go to be at a depth where the turbulence vanished? rad o 4 rad Note: f sin( sin(45 ) 10 4 sec sec (a) b 1 k f 10 U (b) s kg N CD( U ) (10 ).5 sec N.5 o.5,45 to Northeast fk 3 kg sec 3
17 ( c ) z u U ep[ bz]cos( bz.5ep[ ]cos( ) *.70* sec 5 5 v U ep[ bz]sin( bz.5ep[ ]sin( ) *.70* sec v 5 o tan( u 14 u k = kub ep( bz)[cos( bz sin( bz ] z s ep( bz)[cos( bz sin( bz ] = ep( )[cos( sin( ] N =.061
18 v k = kub ep( bz)[cos( bz sin( bz ] z s ep( bz)[cos( bz sin( bz ] = ep( )[cos( sin( ] N =.163
19 ( c ) at z u U ep[ bz]cos( bz.5ep[ ]cos( ) *.3*.8.05 sec 0 0 v U ep[ bz]sin( bz.5ep[ ]sin( ) *.3*(.6).03 sec v 0 tan( u 14 u k = kub ep( bz)[cos( bz sin( bz ] z s ep( bz)[cos( bz sin( bz ] = ep( )[cos( sin( ] N =.059 o
20 v k = kub ep( bz)[cos( bz sin( bz ] z s ep( bz)[cos( bz sin( bz ] = ep( )[cos( sin( ] N =.008 (d) u*=.5 at z=0,.5 u*= sec
21 at z=5, u*= sec at z=0, u*= sec N N ( e) z 1 b
22 v k z 45 o fu 1 z u k z 1 fv z Subsurface Stress Surface Stress Surface Current
23 Approach Using Cople Variables 1 u 1 v fv ; k fu ; k z z z z u fv k & fu k z Let u u iv i=sqrt(-1)=ep( i) u ifu k Solution u Aep( sz) z s v z ep( i) f if if f s = ep( i) (1 i) b k k k 4 k f f b = & s b k k
24 Case 1 ( z 0) 0; ( z 0) 0 (Wind to North) u k As ep( sz) z f Re( ) z0 0 Re( As) Re{ Aep( i) } 0 4 k A Uep( i) u Uep( i)ep( sz) u Re( u) v Iag( u) 4 4 u ep( bz) =( u*) z0 ep( bz) z ( u*) k U s ( u*) U fk z0
25 Case ( u*) k ( z 0) 0; ( z 0) 0 (Wind to East) u k As ep( sz) z f Iag( ) z0 0 Iag( As) Iag{ Aep( i) } 0 4 k A Uep( i) u Uep( i)ep( sz) u Re( u) v Iag( u) 4 4 u U s ep( bz) =( u*) z0 ep( bz) z U ( u*) z0 fk
26 Ekan Dnaics: Botto Laer North u g Sea surface slopes Upward to south 45 o p 0 Assuptions Stead State Upper Ocean Geostrophic u g 1 p 1 fv ( )+ z fu u =k z v =k z 1 p f 0 1 p 1 ( ) 0 Deep Ocean 0 0 Edd Viscosit z East
27 Case 1: Pressure Gradient to North Equations u fv k z v fu fug k z View Looking Down North u u u [1 ep( bz)cos( bz] g v u ep( bz)sin( bz g Solutions f b= bh>>1 k 45 o Note z positive upward b b u fk g u g East
28 Equations u fv fvg k z v fu k z Case : Pressure Gradient to West u v ep( bz)sin( bz g v v [1 ep( bz)cos( bz] g Solutions Solutions f b= bh>>1 k View Looking Down 45 o u v g North b b East v fk g
29 (a) Eaple: At a latitude of under no wind conditions the geostrophic current is observed to be.5 /sec to the east. Observations show that the edd viscosit is - k = 10 sec o 45 N (a) What is the agnitude and direction of the sea surface slope? (b) What is the effective Ekan depth? (c) What is the agnitude and direction of the stress and current on the botto, at z = 0, at = 0,at z = 40? (d) Estiate the turbulent velocit at z = 0, 5, 0. (e) How shallow would ou have to go to be at a depth where the turbulence vanished? p = gz ( p fu = g sec.5 1 p fu - = sec 0 g 10 sec = (b) k 10 f b = = =0-4
30 (c) b u fk g to the northeast u v 0 at z =0 N u u [1 ep( bz)cos( bz] g v u ep( bz)sin( bz g u k kugb ep( bz)[cos( bz sin( bz)] z b ep( bz)[cos( bz sin( bz)] v k kugb ep( bz)[cos( bz sin( bz)] z b ep( bz)[cos( bz sin( bz)]
31 At z =0 0 u ug[1 ep( bz)cos( bz].5(1 ep( )cos(1).4 0 sec 0 v ug ep( bz)sin( bz.5(ep( )sin(1).15 0 sec b.7 ep( bz)[cos( bz sin( bz)] ep( 1)[cos(1 sin(1)] N =.5 b.7 ep( bz)[cos( bz sin( bz)] ep( 1)[cos(1 sin(1)] N -.05
32 At z =40 u ug[1 ep( bz)cos( bz].5[1 ep( )cos()].5 sec v ug ep( bz)sin( bz.5(ep( )sin().056 sec b.7 ep( bz)[cos( bz sin( bz)] ep( )[cos( sin()] N =.033 b.7 ep( bz)[cos( bz sin( bz)] ep( )[cos( sin()] N.09 At z =0,0, 40 N.5,.5,09 (d) u*.0,.0158,.0095 sec
33 Pressure Gradient Force Force Balance 45 o Geostroph fu g 1 p F p Botto Stress B u g kf B North U g U East fv fu Ekan Dnaics 1 z 1 p 1 ( )+ z Note: Forces are obtained b a vertical integral of above equations Coriolis Force F Co
34 Botto Transport Anoal (V) depth u g p depth u g East North North V ugb V -1 East 45 o z 0 ugb V u g f ( u ug) fu p Let v=( u u ) g g 0 z dz z 0 dz f ( u ug) z o z 0 k u fv V ug f o g b -1
ESCI 485 Air/sea Interaction Lesson 5 Oceanic Boundary Layer
ESCI 485 Air/sea Interaction Lesson 5 Oceanic Boundar Laer References: Descriptive Phsical Oceanograph, Pickard and Emer Introductor Dnamical Oceanograph, Pond and Pickard Principles of Ocean Phsics, Apel
More informationChapter 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
More informationOcean Dynamics. The Equations of Motion 8/27/10. Physical Oceanography, MSCI 3001 Oceanographic Processes, MSCI dt = fv. dt = fu.
Phsical Oceanograph, MSCI 3001 Oceanographic Processes, MSCI 5004 Dr. Katrin Meissner k.meissner@unsw.e.au Ocean Dnamics The Equations of Motion d u dt = 1 ρ Σ F Horizontal Equations: Acceleration = Pressure
More informationOcean Dynamics. Equation of motion a=σf/ρ 29/08/11. What forces might cause a parcel of water to accelerate?
Phsical oceanograph, MSCI 300 Oceanographic Processes, MSCI 5004 Dr. Ale Sen Gupta a.sengupta@unsw.e.au Ocean Dnamics Newton s Laws of Motion An object will continue to move in a straight line and at a
More informationOCN/ATM/ESS 587. The wind-driven ocean circulation. Friction and stress. The Ekman layer, top and bottom. Ekman pumping, Ekman suction
OCN/ATM/ESS 587 The wind-driven ocean circulation. Friction and stress The Ekman layer, top and bottom Ekman pumping, Ekman suction Westward intensification The wind-driven ocean. The major ocean gyres
More informationSIO 210 Problem Set 3 November 15, 2013 Due Nov. 22, 2013 Answerkey
SIO 210 Problem Set 3 November 15, 2013 Due Nov. 22, 2013 Answerkey 1. Dynamics: rotation (a) Draw the direction of an inertial current in (i) the northern hemisphere and (ii) the southern hemisphere and
More informationThe General Circulation of the Oceans
The General Circulation of the Oceans In previous classes we discussed local balances (Inertial otion, Ekman Transport, Geostrophic Flows, etc.), but can we eplain the large-scale general circulation of
More informationPhysical 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
More informationModels of ocean circulation are all based on the equations of motion.
Equations of motion Models of ocean circulation are all based on the equations of motion. Only in simple cases the equations of motion can be solved analytically, usually they must be solved numerically.
More informationDynamics 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 informationSurface 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
More informationThe 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 informationThe wind-driven models of Stommel and Munk employed a linearization involving a small parameter, the Rossby number, which we need to reconsider.
Equatorial twists to mid-latitude dnamics As we saw or Stommel s or Munk s wind-driven gres and or Sverdrup s balance, there was no particular problem with the equator. In act, Stommel solved his gre or
More informationCombined tidal and wind driven flows and residual currents
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Combined tidal and wind driven flows and residual currents 1 Lars Erik Holmedal, Hong Wang Abstract : The effect of a residual current on the combined
More information( ) = 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
More informationActual bathymetry (with vertical exaggeration) Geometry of the ocean 1/17/2018. Patterns and observations? Patterns and observations?
Patterns and observations? Patterns and observations? Observations? Patterns? Observations? Patterns? Geometry of the ocean Actual bathymetry (with vertical exaggeration) Continental Continental Basin
More informationConcept of Reynolds Number, Re
Concept of Reynold Nuber, Re Ignore Corioli and Buoyancy and forcing Acceleration Advection Preure Gradient Friction I II III IV u u 1 p i i u ( f u ) b + u t x x x j i i i i i i U U U? U L L If IV <
More informationEffective Depth of Ekman Layer.
5.5: Ekman Pumping Effective Depth of Ekman Layer. 2 Effective Depth of Ekman Layer. Defining γ = f/2k, we derived the solution u = u g (1 e γz cos γz) v = u g e γz sin γz corresponding to the Ekman spiral.
More informationDynamics 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
More informationOscillatory Hydromagnetic Couette Flow in a Rotating System with Induced Magnetic Field *
CHAPTER-4 Oscillator Hdroagnetic Couette Flow in a Rotating Sste with Induced Magnetic Field * 4. Introduction Lainar flow within a channel or duct in the absence of agnetic field is a phenoenon which
More informationEART164: 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 informationReynolds 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= 1.49 m/s m. 2 kg. 2 kg
5.6. Visualize: Please refer to Figure Ex5.6. Solve: For the diagra on the left, three of the vectors lie along the axes of the tilted coordinate sste. Notice that the angle between the 3 N force and the
More informationEquatorial Superrotation on Tidally Locked Exoplanets
Equatorial Superrotation on Tidally Locked Exoplanets Adam P. Showman University of Arizona Lorenzo M. Polvani Columbia University Synopsis Most 3D atmospheric circulation models of tidally locked exoplanets
More informationLecture 25: Ocean circulation: inferences from geostrophic and thermal wind balance
Lecture 25: Ocean circulation: inferences from geostrophic and thermal wind balance November 5, 2003 Today we are going to study vertical sections through the ocean and discuss what we can learn about
More informationInternal boundary layers in the ocean circulation
Internal boundary layers in the ocean circulation Lecture 9 by Andrew Wells We have so far considered boundary layers adjacent to physical boundaries. However, it is also possible to find boundary layers
More informationLecture 17 ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY. Learning objectives: understand the concepts & physics of
ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY Lecture 17 Learning objectives: understand the concepts & physics of 1. Ekman layer 2. Ekman transport 3. Ekman pumping 1. The Ekman Layer Scale analyses
More informationOcean dynamics: the wind-driven circulation
Ocean dynamics: the wind-driven circulation Weston Anderson March 13, 2017 Contents 1 Introduction 1 2 The wind driven circulation (Ekman Transport) 3 3 Sverdrup flow 5 4 Western boundary currents (western
More informationLecture 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
More information2.5 Shallow water equations, quasigeostrophic filtering, and filtering of inertia-gravity waves
Chapter. The continuous equations φ=gh Φ=gH φ s =gh s Fig..5: Schematic of the shallow water model, a hydrostatic, incompressible fluid with a rigid bottom h s (x,y), a free surface h(x,y,t), and horizontal
More information7 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,
More informationChapter 9. Geostrophy, Quasi-Geostrophy and the Potential Vorticity Equation
Chapter 9 Geostrophy, Quasi-Geostrophy and the Potential Vorticity Equation 9.1 Geostrophy and scaling. We examined in the last chapter some consequences of the dynamical balances for low frequency, nearly
More informationDynamic 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 informationESCI 485 Air/Sea Interaction Lesson 1 Stresses and Fluxes Dr. DeCaria
ESCI 485 Air/Sea Interaction Lesson 1 Stresses and Fluxes Dr DeCaria References: An Introduction to Dynamic Meteorology, Holton MOMENTUM EQUATIONS The momentum equations governing the ocean or atmosphere
More informationSIO 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.)
More informationOcean surface circulation
Ocean surface circulation Recall from Last Time The three drivers of atmospheric circulation we discussed: Differential heating Pressure gradients Earth s rotation (Coriolis) Last two show up as direct
More information1.1 The Equations of Motion
1.1 The Equations of Motion In Book I, balance of forces and moments acting on an component was enforced in order to ensure that the component was in equilibrium. Here, allowance is made for stresses which
More informationSIO 210: Dynamics VI (Potential vorticity) L. Talley Fall, 2014 (Section 2: including some derivations) (this lecture was not given in 2015)
SIO 210: Dynamics VI (Potential vorticity) L. Talley Fall, 2014 (Section 2: including some derivations) (this lecture was not given in 2015) Variation of Coriolis with latitude: β Vorticity Potential vorticity
More informationSIO 210 Problem Set 2 October 17, 2011 Due Oct. 24, 2011
SIO 210 Problem Set 2 October 17, 2011 Due Oct. 24, 2011 1. The Pacific Ocean is approximately 10,000 km wide. Its upper layer (wind-driven gyre*) is approximately 1,000 m deep. Consider a west-to-east
More informationPhysical 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 =
More informationg (z) = 1 (1 + z/a) = 1
1.4.2 Gravitational Force g is the gravitational force. It always points towards the center of mass, and it is proportional to the inverse square of the distance above the center of mass: g (z) = GM (a
More informationBalanced Flow Geostrophic, Inertial, Gradient, and Cyclostrophic Flow
Balanced Flow Geostrophic, Inertial, Gradient, and Cyclostrophic Flow The types of atmospheric flows describe here have the following characteristics: 1) Steady state (meaning that the flows do not change
More informationInertial Instability. 1. Perspective from the Horizontal Equations of Motion (Momentum Equations) x component. y component
Inertial Instability The following is not meant to be a self-contained tutorial. It is meant to accompany active discussion and demonstration in the classroom. 1. Perspective from the Horizontal Equations
More informationThe California current is the eastern boundary current that lies to the west of
I. INTORDUCTION A. California Current System The California current is the eastern boundary current that lies to the west of North America. The California current flows from north, Washington, to south,
More informationDiscretization- Finite difference, Finite element methods
Discretization- Finite difference, Finite element methods Q. Identify the natural and essential boundary conditions of the following differential equation: d d y a( ) b( ) + =, for < < ; subject to the
More informationThe 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 informationTreatment of Earth as an Inertial Frame in Geophysical Fluid Dynamics. Dana Duke
Treatment of Earth as an Inertial Frame in Geophysical Fluid Dynamics Dana Duke PHGN 505 Term Paper December 2011 Dana Duke 1 Abstract The purpose of this paper is to introduce how phenomena in geophysical
More informationNote that Rossby waves are tranverse waves, that is the particles move perpendicular to the direction of propagation. f up, down (clockwise)
Ocean 423 Rossby waves 1 Rossby waves: Restoring force is the north-south gradient of background potential vorticity (f/h). That gradient can be due to either the variation in f with latitude, or to a
More informationDust 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 informationOcean 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)
More informationExamples 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 informationSIO 210 Final examination Wednesday, December 12, :30-2:30 Eckart 227 Name:
SIO 210 Final examination Wednesday, December 12, 2018 11:30-2:30 Eckart 227 Name: Please put your initials or name on each page, especially if you pull pages apart. Turn off all phones, ipods, etc. and
More information+ ω = 0, (1) (b) In geometric height coordinates in the rotating frame of the Earth, momentum balance for an inviscid fluid is given by
Problem Sheet 1: Due Thurs 3rd Feb 1. Primitive equations in different coordinate systems (a) Using Lagrangian considerations and starting from an infinitesimal mass element in cartesian coordinates (x,y,z)
More informationOcean 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
More informationEarth s Environmental System: Climate V2100. Midterm Exam. Wednesday March 12, 2003
Earth s Environmental System: Climate V2100 Midterm Exam Wednesday March 12, 2003 Please put your name at the top of each page If you sketch something, make it big and clear and label your axes Explain
More informationHomework 2: Solutions GFD I Winter 2007
Homework : Solutions GFD I Winter 007 1.a. Part One The goal is to find the height that the free surface at the edge of a spinning beaker rises from its resting position. The first step of this process
More information2 A: The Shallow Water Equations
2 A: The Shallow Water Equations 2.1 Surface motions on shallow water Consider two-dimensional (x-z) motions on a nonrotating, shallow body of water, of uniform density, as shown in Fig. 1 below. The ow
More informationFundamental Meteo Concepts
Fundamental Meteo Concepts Atmos 5110 Synoptic Dynamic Meteorology I Instructor: Jim Steenburgh jim.steenburgh@utah.edu 801-581-8727 Suite 480/Office 488 INSCC Suggested reading: Lackmann (2011), sections
More informationChapter 5. Shallow Water Equations. 5.1 Derivation of shallow water equations
Chapter 5 Shallow Water Equations So far we have concentrated on the dynamics of small-scale disturbances in the atmosphere and ocean with relatively simple background flows. In these analyses we have
More information7. TURBULENCE SPRING 2019
7. TRBLENCE SPRING 2019 7.1 What is turbulence? 7.2 Momentum transfer in laminar and turbulent flow 7.3 Turbulence notation 7.4 Effect of turbulence on the mean flow 7.5 Turbulence generation and transport
More information10 Shallow Water Models
10 Shallow Water Models So far, we have studied the effects due to rotation and stratification in isolation. We then looked at the effects of rotation in a barotropic model, but what about if we add stratification
More informationBALANCED 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
More informationGeostrophy & 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
More informationacceleration of 2.4 m/s. (b) Now, we have two rubber bands (force 2F) pulling two glued objects (mass 2m). Using F ma, 2.0 furlongs x 2.0 s 2 4.
5.. 5.6. Model: An object s acceleration is linearl proportional to the net force. Solve: (a) One rubber band produces a force F, two rubber bands produce a force F, and so on. Because F a and two rubber
More informationPart-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 informationAtmosphere, 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
More informationChapter 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 informationChapter 7: Circulation and Vorticity
Chapter 7: Circulation and Vorticity Circulation C = u ds Integration is performed in a counterclockwise direction C is positive for counterclockwise flow!!! Kelvin s Circulation Theorem The rate of change
More informationGoal: Use understanding of physically-relevant scales to reduce the complexity of the governing equations
Scale analysis relevant to the tropics [large-scale synoptic systems]* Goal: Use understanding of physically-relevant scales to reduce the complexity of the governing equations *Reminder: Midlatitude scale
More informationisopycnal outcrop w < 0 (downwelling), v < 0 L.I. V. P.
Ocean 423 Vertical circulation 1 When we are thinking about how the density, temperature and salinity structure is set in the ocean, there are different processes at work depending on where in the water
More informationIsland Wakes in Shallow Water
Island Wakes in Shallow Water Changming Dong, James C. McWilliams, et al Institute of Geophysics and Planetary Physics, University of California, Los Angeles 1 ABSTRACT As a follow-up work of Dong et al
More informationDiagnosing Vertical Velocity: The Omega Equation. Robert Todd and Kaushik Srinivasan 15 May 2009
Diagnosing Vertical Velocity: The Omega Equation Robert Todd and Kaushik Srinivasan 15 May 2009 Introduction The vertical velocity is much smaller then the horizontal velocity and therefore, difficult
More informationAtmosphere, 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,
More informationFluid Physics 8.292J/12.330J
Fluid Phsics 8.292J/12.0J Problem Set 4 Solutions 1. Consider the problem of a two-dimensional (infinitel long) airplane wing traeling in the negatie x direction at a speed c through an Euler fluid. In
More informationF = 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,
More information1. The figure shows sea surface height (SSH) anomaly at 24 S (southern hemisphere), from a satellite altimeter.
SIO 210 Problem Set 3 November 16, 2015 1. The figure shows sea surface height (SSH) anomaly at 24 S (southern hemisphere), from a satellite altimeter. (a) What is the name of this type of data display?_hovmöller
More informationd 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( ) (9.1.1) Chapter 9. Geostrophy, Quasi-Geostrophy and the Potential Vorticity Equation. 9.1 Geostrophy and scaling.
Chapter 9 Geostrophy, Quasi-Geostrophy and the Potential Vorticity Equation 9.1 Geostrophy and scaling. We examined in the last chapter some consequences of the dynamical balances for low frequency, nearly
More informationSurface Circulation in the North Atlantic & off of Southern California: Two Models
Surface Circulation in the North Atlantic & off of Southern California: Two Models Objective 1. To become familiar with large scale surface circulation patterns in ocean. 2. To be able to predict current
More informationSIO 210 Final examination Answer Key for all questions except Daisyworld. Wednesday, December 10, PM Name:
SIO 210 Final examination Answer Key for all questions except Daisyworld. Wednesday, December 10, 2008 3-6 PM Name: This is a closed book exam. You may use a calculator. There are two parts: Talley (weighted
More informationHydrostatic 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
More informationScale Analysis of the Equations of Motion
hen are curvature terms important? Important for GCMs and large-scale (global) weather. ere, we consider sub-global scale referred to as synoptic scale. Scale Analysis of the Equations of Motion e use
More informationScale-Adaptive Simulation (SAS) Turbulence Modeling. F.R. Menter, ANSYS Germany GmbH
Scale-Adaptive Simulation (SAS) Turbulence Modeling F.. Menter, ANSYS German GmbH 1 Unstead ANS Based Models UANS (Unstead enolds averaged Navier Stoes) Methods UANS gives unphsical single mode unstead
More informationRoad to Turbulence in Stratified Flow
Road to Turbulence in Stratified Flow (Exaple: Boundary flow with f =0) Lainar Flow U H Turbulent Flow I II III IV V u u p u i i i u b t x x x x b g 0 i N 0 0 g z Turbulence occurs when: II UL R e R eyonlds
More informationLecture 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
More informationExample 1: Example 1: Example 2: a.) the elevator is at rest. Example 2: Example 2: c.) the elevator accelerates downward at 1.
Exaple 1: 60 kg, v 1 100 N (wet), v 2 220 N (eat), a? Exaple 1: wo force parallel to the ground act upon a box with a a of 60 kg. One force i directed wet and ha a trength of 100 N. he other force i directed
More information1. tangential stresses at the ocean s surface due to the prevailing wind systems - the wind-driven circulation and
Chapter 9 The wind-driven circulation [Hartmann, Ch. 7 (7.4-7.5)] There are two causes of the circulation of the ocean: 1. tangential stresses at the ocean s surface due to the prevailing wind systems
More informationThe Boundary Layer and Related Phenomena
The Boundary Layer and Related Phenomena Jeremy A. Gibbs University of Oklahoma gibbz@ou.edu February 19, 2015 1 / 49 Overview Nocturnal Low-Level Jets Introduction Climatology of LLJs Meteorological Importance
More information2.3. PBL Equations for Mean Flow and Their Applications
.3. PBL Equations for Mean Flow and Their Applications Read Holton Section 5.3!.3.1. The PBL Momentum Equations We have derived the Reynolds averaed equations in the previous section, and they describe
More informationOcean Dynamics. The Great Wave off Kanagawa Hokusai
Ocean Dynamics The Great Wave off Kanagawa Hokusai LO: integrate relevant oceanographic processes with factors influencing survival and growth of fish larvae Physics Determining Ocean Dynamics 1. Conservation
More informationMIDTERM 1: APPROXIMATE GRADES TOTAL POINTS = 45 AVERAGE = 33 HIGH SCORE = = A = B = C < 20.0 NP
MIDTERM 1: TOTAL POINTS = 45 AVERAGE = 33 HIGH SCORE = 43 APPROXIMATE GRADES 38.0 45.0 = A 30.0 37.5 = B 20.0 29.5 = C < 20.0 NP Forces to consider: 1) Pressure Gradient Force 2) Coriolis Force 3) Centripetal
More informationLecture 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 informationUpper Ocean Circulation
Upper Ocean Circulation C. Chen General Physical Oceanography MAR 555 School for Marine Sciences and Technology Umass-Dartmouth 1 MAR555 Lecture 4: The Upper Oceanic Circulation The Oceanic Circulation
More information2/15/2012. 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;
More informationFind the indicated derivative. 1) Find y(4) if y = 3 sin x. A) y(4) = 3 cos x B) y(4) = 3 sin x C) y(4) = - 3 cos x D) y(4) = - 3 sin x
Assignment 5 Name Find the indicated derivative. ) Find y(4) if y = sin x. ) A) y(4) = cos x B) y(4) = sin x y(4) = - cos x y(4) = - sin x ) y = (csc x + cot x)(csc x - cot x) ) A) y = 0 B) y = y = - csc
More informationI. Ocean Layers and circulation types
OCEAN Title CIRCULATION slide I. Ocean Layers and circulation types 1) Ocean Layers Ocean is strongly Stratified Consists of distinct LAYERS controlled by density takes huge amounts of energy to mix up
More informationI. Ocean Layers and circulation types
OCEAN CIRCULATION I. Ocean Layers and circulation types 1) Ocean Layers Ocean is strongly Stratified Consists of distinct LAYERS controlled by density takes huge amounts of energy to mix up the stable
More informationAPPLIED MATHEMATICS HIGHER LEVEL
L.42 PRE-LEAVING CERTIFICATE EXAMINATION, 203 APPLIED MATHEMATICS HIGHER LEVEL TIME : 2½ HOURS Six questions to be answered. All questions carry equal marks. A Formulae and Tables booklet may be used during
More informationSpherical Shallow Water Turbulence: Cyclone-Anticyclone Asymmetry, Potential Vorticity Homogenisation and Jet Formation
Spherical Shallow Water Turbulence: Cyclone-Anticyclone Asymmetry, Potential Vorticity Homogenisation and Jet Formation Jemma Shipton Department of Atmospheric, Oceanic and Planetary Physics, University
More informationρ x + fv f 'w + F x ρ y fu + F y Fundamental Equation in z coordinate p = ρrt or pα = RT Du uv tanφ Dv Dt + u2 tanφ + vw a a = 1 p Dw Dt u2 + v 2
Fundamental Equation in z coordinate p = ρrt or pα = RT Du uv tanφ + uw Dt a a = 1 p ρ x + fv f 'w + F x Dv Dt + u2 tanφ + vw a a = 1 p ρ y fu + F y Dw Dt u2 + v 2 = 1 p a ρ z g + f 'u + F z Dρ Dt + ρ
More information