P. N. Vinayachandran Centre for Atmospheric and Oceanic Sciences (CAOS) Indian Institute of Science (IISc) Bangalore 560 012 [email protected] Summer.

P. N. VinayachandranCentre for Atmospheric and Oceanic Sciences (CAOS)

Indian Institute of Science (IISc)Bangalore 560 012

[email protected]

Summer School onDynamics of North Indian Ocean

June-July 2010

OGCM Configuration

OSCAR Currents

Equations of Motion

Spherical Co-ordinate System

r=radius of the earth=latitude=longitude

Equations in Spherical Co-ordinates

Modular Ocean Model

Hydrostatic

Thin shell

Boussinesq

Sub-grid scale processes are represented by eddy mixing coefficients

Water column thickness: D = H +

H(x,y) = Ocean depth; = (x,y,t) is the sea surface deviation from rest (z=0)

Kinematic surface and bottome boundary conditions

At z=-H

At z=

Griffies, 2001, MOM4 guide

Equation for free surface

For a Boussinesq ocean: Assume volume sources/sinks only at the surface lead tobalance of volume per unit area within a ocean column

Ocean surface is affected by three processes:1. Convergence of vertically integrated momentum2. Mass entering through the ocean surface3. Water column dialations due to changes in vertically inegrated density field (steric effects)

Kinematic surface and bottom boundary conditions

At z=-H

At z=

= volume per unit time per unit horizontal area of freshwater crossing the sea surface

= depth integrated horizontal velocity field

Water column thickness: D = H +

Closed Lateral boundaries : no slip, no normal flow

Open lateral boundaries : sponge

Surface dynamic boundary conditions for momentum and freshwater

Bottom drag

Surface heat and fresh water fluxes

Forcing

Smagorinsky viscosityViscosity depends on flow, nonlinearViscosity due to unresolved scales are proportional to (deformation rates X △2)

km is the largest resolvable wave number

How do you choose ?

Deformation rate:

Viscosity:

Let

Then for R < 2

Tracers, Veronis effect, background viscosity

Grid Reynolds No. should be < 2

Griffies, S. M.: Fundamentals of Ocean Climate Models, Princeton University Press, Princeton, USA, 518+xxxiv pages, 2004.

J. Kurian, Ph. D. Thesis, 2007, IISc

Vertical Mixing Schemes

PP KPPMY

Horizontal Grid Size

Rossby radius = cm/f

Equatorail Rossby radius =( cm/)1/2

Eqn. 14.83

m

m

Horizontal grid spacing should resolve the Rossby Radius

Model Domain

Vertical Grid

Topography

ETOPO5, ETOPO2 & modified

Minimum depth of the ocean is 30m. Cells are deepened

Isolated ocean points are converted to land

Palk strait is closed, Red Sea and Persian Gulf are connected to the Arabian Sea, widened to allow 2 grid points

River Runoff

Spin-up

Sigma – coordinates (Princeton Ocean Model)

Mellor, 2002

ROMS

Non-linear stretching of the vertical coordinates depending on local water depth

Haidvogel et al., 2000

Chassignet et al., 2000