Theory and interpretation
Let 'h' be the depth of the fluid, the slope of the bottom, 'L' the side of the square
tank and 'S' the rate at which water is introduced through the diffuser.
The free surface of the water rises at a rate given by:
Because the f
Rigidity imparted to rotating fluids
Take two tanks (of diameter roughly 50 cm) and place one on a rotating table and the
other on a desk. We fill them with water to a depth of 20 cm or so, set the rotating
table turning anticlockwise (looking down from t
Ocean Dynamics: Problem Set 3
Due: Wednesday 20 April 2005
1. PV Homogenization For the two-layer linear quasigeostrophic model, forced by a windstress = 0 cos( y)x, we derived the following solutions for the barotropic PV and
streamfunction: q = y + F an
Ocean Dynamics: Problem Set 2
1. Derive the Barotropic Vorticity Equation
D g
w
+ v g = f 0 ,
Dt
z
where g is the geostrophic vorticity, and state all assumptions clearly (the above is written
in dimensional form, and the geostrophic velocities are for co
Problem Set 1: Ocean Dynamics
Due: Wednesday, 9 February 2005
1. Starting from the primitive equations on the sphere, show that zonal angular momentum
per unit mass m = (u + r cos )r cos is governed by
Dm
1 p
=
.
Dt
Is there an angluar momentum principl
Construction of parabolic turntable
If our cylindrical tank is filled with water, set turning and left until it comes in to solid
body rotation, then the free-surface of the water will not be flat - it will be depressed
in the middle and rise up slightly
Wind-driven ocean circulation
It is relatively straightforward to demonstrate the essential mechanism behind winddriven ocean circulation in a laboratory experiment.
The apparatus is shown in the figure below. A tank with a false sloping bottom is
filled
Thermal Wind Relation and Hadley Circulation
It is straightforward to obtain a steady, axially-symmetric circulation driven by radial
temperature gradients in our laboratory tank, which provides an ideal opportunity to
study the thermal wind relation
We f
Ekman layers
The model for an Ekman layer is geostrophic balance plus wind stress at the surface,
fzu = +
,
z
where = p/0 and is the applied stress divided by the mean density, 0 . Dene the geostrophic
velocity as
1
u g = z .
f
The residual ageostrophic v
The column of dense salty water slumps under gravity but is `held up' by rotation
forming a cone whose sides have a distinct slope. The cone acquires a definite sense
of rotation, swirling cyclonically at its top (in the same sense of rotation as the tabl
An experiment in the Earth's rotation
A classic experiment was carried out by Perrot in 1859 which closely parallels
Foucault's pendulum. He filled a barrel with water (the barrel had a hole in the middle
of its base plugged with a cork) and left it stand
Simplied two-box model of the North Atlantic
This problem develops one of the simplest (and crudest) models for the supposed buoyancy
driven latitudinal and vertical circulation. A truer description of the oceanic overturning circulation, even at the cart
Cloud formation on adiabatic expansion
The sensitive dependence of saturation vapor pressure on temperature can be readily
demonstrated by taking a carboy and pouring warm water in to it to a depth of a few
cms or so, as shown in photograph (lhs). We leav