An OGCM with Movable Land-Sea Boundariesw/Application to Cook Inlet

L. Oey, T. Ezer & M. JohnsonPrinceton Univ. & Univ. Alaska

Goal: A Wetting & Drying (WAD)

scheme that works w/OGCM’s such as the Princeton Ocean

Model (POM)p.2

p.3

p.4

Method: Solve Full 3-D PE (include everything), and impose conditions –

1. WETMASK = 0 for D Hdry,= 1 otherwise.

2. if (Di,j+Di-1,j)/2 Hdry

3. if WETMASKij*WETMASKi-1,j = 0

, 0i jU ,i j

ijkU U

p.5

One-Dimensional WAD Dynamics0 = +

xDU

tD

2+ =

UD U D D H rgD UD

t x x x D

Min , 1r rlD UD

(1a)

(1b)

Condition for friction to dominate is:

Then LHS of (1b) can be dropped, and (1a) & (1b) give:

Typical values: r 10-4~10-3 m/s (in POM, and also Balzano, 1998), 10-4 s-1 (e.g. M2 tide), D = O(1) m, | |U = O(1) m s-1, and l 100’s km for tides.

(2)

(3)2 2

2

22+ = xgDH gD H

r r x

gDD D Dt x x r x

“Advection Velocity”

“Diffusivity” “Sink” if Convex “Source if Concave

Note the possibility of a “breaking-wave” solution

The diffusive penetration distance, Lpd say, at a given time t is proportional to D(g/r)1/2. p.6

A Challenging

(Giant) Water-Fall Problem:

p.7

p.8

Tsunami:

Energy Considerations:

2

1

2 2 2

0

( )lo x

ox

g Bdx B g Du dx

22 2 2

( )2 o

oBDu

g B x

therefore,

Since

and /10m u 14m s

At land-fall,

p.9

Cook Inlet Alaska

p.10

Large Tidal Range Inland

Weak Tides Offshore

p.11

Model of Cook Inlet, Alaska

p.12

Flood Begins @ Upper Inlet

Forcing:

12-hr tide

Rivers

Wind: Anchorage

Nikiski

Drift Riv.

Augustine Is.

p.13

Wetting & Drying:

p.14

Low Tide, River = 0 (i.e. ~ winter)

Anchorage

Skiing

Portage Galcier

1st Picture

Turnagain Arm

Knik Arm

p.15

p.16

Salinity sections in upper CI at low &

high tide

A

B

C

A

B

C

p.17

Salinity & rip tides in central CI

I=140

I=180

Kal

iforn

sky

Bea

ch

1 hr before high tide

p.18

Vertical VelocityW-Contours

Effects of River-Induced Buoyancy on rip tides

w/River Discharge

No River: Climatology only

Homogeneous Water

p.19

ConclusionsAn OGCM with dynamic (movable) land-sea

boundaries has been developed

The model conserves mass & energy and has been tested for idealized and analytical solutions as well as realistic conditions in the Cook Inlet wherein forcing such as tides, winds, rivers were specified

Oey, 2005: A WAD Scheme for POM. Ocean Modelling, 9, 133-150.Oey, 2006: An OGCM w/Movable Land-Sea Boundaries, Ocean

Modelling, in press

Financial supports from MMS, and computing supports from GFDL are gratefully acknowledged. p.20