HW2: 1: Geostrophic current: example calculation
P3P( r )
∂x+ v ∂v
∂z+ fu+ 1
4 Scale analysis:
fU ?? = AxVLx2
WH~ ULx,W ~ UH
10-7 10-6 10-6 10-6 10-5 ?? = 10-5 10-7 10-7
Geostrophy does not hold
2. Arctic – North Atlantic exchange
5. a) NE US coast: SLR?
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
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
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
1. Coastally trapped waves: Continental shelf wavesy
H is depth of water column. Analytic solution, more complicated.
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;
First baroclinic mode:
Phase speed and group velocity of Kelvin waves:
Non-dispersive. Both phase and energy propagate eastward. Exist for all frequencies
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 N.H.
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
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 = −*
'(-= − *
Short Rossby waves:
Phase propagates westward, energy eastward.