ES3013 Fluid Dynamics

What does hydrostatic balance tell you?

that the PGF and gravity (g) roughtly balance eachother in the vertical direction

Which direction does coriolis deflect fluid in relation to direction of motion

to the right in the N. Hemisphere

what is the centrifugal force

the outward force arising from earth’s spin on its axis. At higher latitudes it has an upward and outward motion; at the equator it is perpendicular to the axis of rotation

What does the Rossby number describe?

the relationship between the coriolis and inertial forces

what does a small Rossby number indicate

strong Coriolis weak acceleration terms

What does a large rossby number indicate

weak coriolis and strong acceleration — geostrophic balance doesn’t hold

what is the significance of a small Rossby number

the coriolis dominates and thus the acceleration term can be ignored in the horizontal momentum equation — therefore we have geostrophic balance!

What is geostrophic balance

the PGF is balanced by the coriolis force, allowing movement of a fluid to be along isobars (lines of constant pressure)

what are the assumptions of geostrophic balance?

steady state, no friction, hydrostatic vertical balance

What is the weakness of geostrophic flow

it’s non divergent (the same everywhere) so it tell us nothing about vertical motion

How does pressure change with temperature

pressure decreases from warm → cold

What does thermal wind describe

the change (shear) caused by horizontal temp gradients — a stronger shear is associated with stronger temp gradients

How does density vary in the ocean

it’s safe to assume that density is constant in oceans because the actual difference between the warmest/freshest and the coolest/saltiest is <1%

In the ocean, where is pressure highest?

at the poles where there is the highest sea level

Does geostrophic balance apply in oceans?

Yes! it’s a better approximation in oceans than in atmosphere b/c Rossby number is even smaller (coriolis force is more dominant)

when is friction important

within 1km of the atmosphere and the top 100m of the ocean

what does Ekman balance do

takes into account friction — when friction drags the velocity (u), it is balanced by the Coriolis and shifts direction of flow slightly in toward a low pressure system

what does Ageostrophic velocity describe

coriolis balances wind force

what are the affects of Ekman balance

causes convergence and convection (rising) in low pressure systems and divergence (sinking) in high pressure system

how does Ekman balance affect Mass transport

the net transport is perpendicular to wind direction in the Ekman layer — a combination of coriolis and wind stress

convergence in ekman layer

pumping (downwelling)

divergence in ekman layer

suction (upwelling)