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SCALING AND NON-DIMENSIONAL NUMBERSPowerPoint Presentation

SCALING AND NON-DIMENSIONAL NUMBERS

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For example: ratio of Inertia to Rotation

For Ro << 1, e.g., Ro ~ 0.01, inertial accelerations are negligible and the motion is “linear”

Example: U = 0.1 m/s, f = 10-4 s-1, L = 10 km

For Ev << 1, e.g., Ev ~ 0.01, frictional effects are negligible and the motion is dominated by Coriolis accelerations

Example: Ax = 103 m2/s, f = 10-4 s-1, L = 10 km

Example: Az = 10-3 m2/s, f = 10-4 s-1, H = 10 m

Scaling is very important to help us diagnose the relevant forces driving the flow in a given area

(horizontal momentum).

Local Inertial Coriolis Pres. Grad Hor. Fric. Ver. Fric.

t = 12 h ~ 104 s ; Ax = 103 m2/s; Az = 10-2 m2/s

For vertical momentum the concern is with the stability of the water column (density distribution with depth)

Perturbations to the pycnocline (region of maximum stability) cause oscillations.

The frequency of the oscillations (radians / s) is given by:

Buoyancy Frequency or Brunt-Väisälä Frequency

A stable water column does not necessarily represent zero vertical exchange of properties

Salt Fingers stability) cause oscillations. Experiment

http://www.phys.ocean.dal.ca/programs/doubdiff/labdemos.html

Example of Salt Fingers (Kuroshio waters interacting with waters from Sea of Japan – through Tsugaru Strait)

AIST Japan

From Miyake et al. (1995, Journal of Oceanogr., 51, 99-109)

Requirements for Salt Fingers: waters from Sea of Japan – through Tsugaru Strait)

a) dS/dz > 0

dT/dz > 0

b) Small density ratios

c) Staircase in profiles

From Miyake et al. (1995, Journal of Oceanogr., 51, 99-109)

From Miyake et al. (1995, Journal of Oceanogr., 51, 99-109) waters from Sea of Japan – through Tsugaru Strait)

From Miyake et al. (1995, Journal of Oceanogr., 51, 99-109) waters from Sea of Japan – through Tsugaru Strait)

heat flux waters from Sea of Japan – through Tsugaru Strait)

from below

Layering Experiment

http://www.phys.ocean.dal.ca/programs/doubdiff/labdemos.html

Data from the Arctic waters from Sea of Japan – through Tsugaru Strait)

From Kelley et al. (2002, The Diffusive Regime of Double-Diffusive Convection)

SHEARED FLOW AND STRATIFICATION waters from Sea of Japan – through Tsugaru Strait)

Click on image to see animation

May cause instabilities like the one above (Kelvin-Helmholtz)

Richardson waters from Sea of Japan – through Tsugaru Strait)

Number

What will determine whether these waves become unstable?

Overall Richardson Number waters from Sea of Japan – through Tsugaru Strait)

Ri < 0.25 necessary condition for instabilities to develop

(0.30 from observations in natural environments)

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