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  • HW2: 1: Geostrophic current: example calculation

    P2

    P3P( r )

    A B

    0db

    400db

    500db

    Northern Hemisphere

    PGF CF

    0

    �A =

    Z 1000

    500�Adp

    �B =

    Z 1000

    500�Bdp

    400dbar

    .

  • ∂v∂t+u ∂v

    ∂x+ v ∂v

    ∂y+w ∂v

    ∂z+ fu+ 1

    ρ∂p∂y

    = Ax∂2v∂x2

    + Ay∂2v∂y2

    + Az∂2v∂z2

    4 Scale analysis:

    VT

    UVLx

    V 2

    LyWVH

    fU ?? = AxVLx2

    AyVLy2

    AzVH 2

    WH~ ULx

    WH~ ULx,W ~ UH

    Lx~10−3

    10-7 10-6 10-6 10-6 10-5 ?? = 10-5 10-7 10-7

    fu+ 1ρ∂p∂y

    = Ax∂2v∂x2

    Geostrophy does not hold

  • 2. Arctic – North Atlantic exchange

    5. a) NE US coast: SLR?

    A B

    USA 1b) (Critical thinking) Do you expect the subtropical gyre of the North Atlantic spin up (intensifying) or spin down (weakening), and why? (5pts)

    1c) (Critical thinking) Recent climate model studies suggest that global warming accelerates the SLR along the US Northeast coast. Do you expect an intensified or weakened Atlantic Meridional Overturning Circulation, and why? (5pts)

  • ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY

    Lecture 14

    1. Coastally trapped waves: continental Shelf Waves (continue)

    2. Equatorial waves: (i) Equatorial Kelvin wave;(ii) EQ Rossby wave;(iii) EQ IGW;(iv) Mixed Rossby-gravity wave – Yanai wave

    Learning objectives: understand the characters (e.g. energy dispersion, solution, excitation) of the

    following waves

  • Figure: satellite Observed Sea Surface Height anomalies (SSHA) over the Bay of Bengal of the Indian Ocean: coastal Kelvin waves propagate from the eastern equatorial Indian Ocean to the Bay of Bengal (Rao et al. 2010, DSR)

    Coastal Kelvin waves: propagate with the coast to its right (left) in Northern (Southern) hemisphere.Solutions are trapped to the coast, decaying away from it exponentially, with an e-folding scale of the Rossby radius of

    deformation.

    Previous class:

  • 1. Coastally trapped waves: Continental shelf wavesy

    Coast

    shallow

    deep

    x

  • z

    y

    H(y)Deep water

    Shelf

  • H is depth of water column. Analytic solution, more complicated.

    acts as

    Topographic Rossby waves

  • Shelf waves: dispersive.

    Propagation: like coastal Kelvin waves;

    Mechanism: like Rossby waves: Potential vorticityconservation:

    Here, H varies with y because of the shelf;Near the coast, scale is small,

  • NH, North Coast

  • 2. Equatorial waves(i) The equatorial Kevin wave

    a) Dispersion relation:

    barotropic or baroclinic mode speed;

    Barotropic mode:

    First baroclinic mode:

  • Phase speed and group velocity of Kelvin waves:

    Non-dispersive. Both phase and energy propagate eastward. Exist for all frequencies

    ω

  • b) Solution:

    E-folding scale:

    Equatorially-trapped: due to c) Symmetric about the equator (u and p/sea level)d) Forcing. Changing winds with time – symmetric

    about the EQ.

    EQ y=0

    EQ y>0 N.H.

    EQ y

  • Equatorial Kelvin wave structure

    Red contours: Symmetric about the equator for Sea surface height (SSH)

  • Satellite-observed sea surface height anomalies

    Propagation: direction? Eastward

  • Westerly wind burst (WWB) associated with the Madden-Julian Oscillation (MJO):

    T=t1 T=t2 EastEQWestEQ

    Equatorial (EQ) westerly wind burst

  • WWB, EQ Kelvin wave &onset of the 1997 El Nino

  • 3. Equatorial Rossby wavesa) Dispersion relation

    Here, 𝑙=1,2,3,….is the order number of Hermite function in y direction. Often called “meriodinal mode” number.

    Long Rossby waves:

    𝜔 = −𝛽𝑘

    𝑘'()*(',(-)

    𝜔=- *',(-

    𝑘As before, c is either a baroclinic or barotropic mode speed.

  • Long Rossby waves: non-dispersive.Propagates westward. The fastest speed for a baroclinic mode is for 𝑙=1 (first meridional mode Rossby wave):

    Which is 1/3 of Kelvin wave speed. So, Rossby waves propagate slower than Kelvin waves

    𝑐0 = 𝑐1 = −*

    ',(-

    𝑐0 = 𝑐1 = −*

    '(-= − *

    2.

  • Short Rossby waves:

    Phase propagates westward, energy eastward.