You are on an oceanographic cruise at the equator (i.e. Coriolis force is zero).

Question

You are on an oceanographic cruise at the equator (i.e. Coriolis force is zero). You measure the potential density at station A to be 1025 kg/m3 between 0 and 200m depth and you measure the potential density at station B to be 1027 kg/m3 between 0 and 200m depth. The sea surface height at station A is 10 cm higher than at station B. Station B is 100 km directly to the East of station A.

a) Calculate the pressure at 10 cm depth at A and at the surface at B (which are at equal heights). Note: Assume Patm is equal at both stations and thereby can be ignored.

b) What is the magnitude and direction of the acceleration between 10 cm depth at A and the surface at B?

c) What is the magnitude and direction of the acceleration between A at 200.1m and B at 200m (equal heights)?

d) Calculate the depth where the pressure gradient induces no motion.

e) Now, assume you are now North of the equator and Coriolis force is not zero. What direction

will the current at the surface go? What direction will the current at 200m go?

Explanation / Answer

a)             Calculate the pressure at 10 cm depth at A and at the surface at B (which are at equal heights). Note: Assume Patm is equal at both stations and thereby can be ignored.

r = density at A between 0 and 200m depth of Ocean = 1025 kg/m³

g = acceleration of gravity = 9.8 m/s2   

h = height of water at A     = 10 cm = 0.10m

The formula that gives the P pressure on an object submerged in a fluid is:

P = r * g * h

         P = 1025 x 9.8 x 0.10 = 1,004.5 newton’s/m²

b)             What is the magnitude and direction of the acceleration between 10 cm depth at A and the surface at B?

The pressure at 10 cm depth at A and B locations is same. So there is no flow of water and there is no magnitude and direction of acceleration.

c)             What is the magnitude and direction of the acceleration between A at 200.1m and B at 200m (equal heights)?

The Ocean depth at A is 200.1 m

The ocean depth at B is 200.0 m

So at A the ocean has 10 cm more depth then B

So the direction of acceleration is from B to A, that is due East

Magnitude is pressure = 1.004.5 newton’s/m²

d)             Calculate the depth where the pressure gradient induces no motion.

The pressure gradient induce no motion is at 200.0 m depth

e)             Now, assume you are now North of the equator and Coriolis force is not zero. What direction will the current at the surface go? What direction will the current at 200m go?

The current at surface will go in west direction when in north of equator where Coriolis force is acting.

Here at 200 m depth the current direction is in west same as on surface.

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