# ENVS366_1x

Mechanics

Oct 24, 2013 (4 years and 8 months ago)

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Marine Turbulence and Mixing

Dr. Matthew Palmer

matthew.palmer@noc.ac.uk

1.
Introduction

Monday 21
st

9
-
10am

2.
Turbulence theory

Monday 21
st

11
-
12am

3.
Measuring turbulence

Monday 28
th

9
-
10am

4.
Modelling turbulence

Monday 28
th

11
-
12am

1. Introduction

Why is turbulent mixing important?

Turbulent mixing in ocean underpins many of the
critical components in our Earth system.

Ventilating oceans.

Promoting biological growth.

Controlling climate.

?

Convective instability

Shear driven instability

Sources of mixing in the ocean

wind

waves

Tides?

Biology?

Topography

Mechanisms:

Definition of turbulence:

Random
, chaotic, irregular and unpredictable.

Vortical
.

3
-
dimensional
.

Dissipative
, always.

, unstable. Occurring over a broad
spectrum of length and time scales.

Diffusive
. Promoting enhanced transfer by
mixing.

The transition from laminar flow to turbulence (Thorpe, 1971)

Moum

et al
, JPO, 2003

S.A. Thorpe, 1971: Journal of Fluid Mechanics

, 46 : pp 299
-
319

Tank experiment: shear driven instability

Calculating the consequences of mixing:

r
1

r
0

r
2

PE
0

PE
1

Change in potential energy

D
PE = PE
1

PE
0

PE
1
=
r
2
h
gh
/2 =
r
2
h
2
g/2

PE
0

= PE(bottom) + PE(top)

= [(h
-
h
1
)
r
0

g (h
-
h
1
)/2] + [h
1

r
1

g (h
-
(h
1
/2))]

h

h
1

Due to the conservation of mass,

r
2
h =
r
0

(h
-
h
1
) +
r
1

h
1

, but
r
1

=
r
0

D
r

So,

r
2
h =
r
0

(h
-

h
1
) + (
r
0

D
r
)

h
1

=

Potential Energy (PE) = mass x g x height (centre of mass)

Consider PE per unit area by calculating mass/unit area =
r

x h

r
0
h
-

D
r
h
1

r
2

=
r
0

D
r

h
1
/h

(J m
-
2
)

To the labs!