Lecture on Oceanography by Victor Zhurbas
LECTURE 7. OCEANIC FINE STRUCTURE
Oceanic finestructure can be simply defined as the irregularities of the vertical size of
one meter to one hundred meters which are usually observed on vertical profiles of
temperature, salinity, density, velocity, a passive tracer concentration, etc. in the ocean.
In contrast to turbulent fluctuations, the finestructure fluctuations are strongly
anisotropic: their horizontal length scale is usually a factor 100-1000 larger than the vertical
length scale.
The minimum vertical length scale of finestructure is just restricted by the Ozmidov scale
L0 = (ε / N 3 ) 1/ 2 . As to the maximum vertical length scale of finestructure, we cannot define it
more or less strictly; and we usually have some liberty in the way to define it.
Finestructure in temperature, salinity, and density fields is called the thermohaline
finestructure. Here, we will consider just thermohaline oceanic finestructure.
They say it is better to see once than 10 times to hear, so we start our acquaintance with
the thermohaline finestructure with some examples.
Lecture on Oceanography by Victor Zhurbas
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7.0
8.0
9.0
10.0
11.0
S, psu
3.0
3.5
4.0
4.5
5.0
T,°C
70
90
110
130
150
170
σθ
P,
S
T
dbar
4.0
5.0
6.0
7.0
8.0
9.0
σ, kg m-3
7.0
8.0
9.0
10.0
11.0
12.0
S, psu
5.5
5.0
4.5
4.0
3.5
T,°C
Fig.6.1. Vertical profiles of temperature, salinity, and density in the
Baltic halocline.
Fig.6.1 shows vertical profiles of temperature, salinity, and density in the Baltic halocline.
Note, the temperature finestructure is more “visible” than that of salinity and density. There are a
lot of inversions in temperature, and none of them in salinity and density. Note, that finestructure
appearance in salinity resembles well that of density.
Lecture on Oceanography by Victor Zhurbas
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Temperature, C
7
8
9
10
11
12
13
14
15
16
200
250
300
350
400
450
T
S
Z, m
500
34.8
35.0
35.2
35.4
35.6
35.8
36.0
36.2
36.4
salinity, psu
Fig.6.2. Step-like finestructure in the Northwest Tropical Atlantic
In Fig.6.2, on can see an extremely regular stepped finestructure from the Northwest
Tropical Atlantic. Density (not shown) is steplike as well, but the deeper layer the larger density
be.
15
16
17
18
19
20
21
22
23
24
25
26
27
80
T,C
90
100
110
120
130
140
150
T
S
160
170
Z,m
S, psu
180
35.4
35.5
35.6
35.7
35.8
35.9
36.0
36.1
36.2
36.3
Fig.6.3. Vertical profiles of temperature and salinity in the Northwest
Atlantic, in the Gulf Stream frontal zone
Lecture on Oceanography by Victor Zhurbas
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In Fig.6.3 one can see a finestructure in which there are a lot of well-pronounced
inversions in salinity, and only very weak inversions in temperature - just to the contrary to
Fig.6.1 where there were a lot of inversions in temperature and no one in salinity.
In Fig.6.4 one can see a two-dimensional picture of finestructure, taken by a tow-yo CTD
in the Baltic Sea.
-50
5.4
5.2
5.0
4.8
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
60
depth, m
-100
100
-150
140
Z, m
180
-200
60
a
Temperature,
C
0
10
20
30
40
50
60
70
80
90
100 110 120 130 140 150 160
distance, km
100
140
Z, m
b
0
20
40
60
80
100
120
140
L, km 160
Fig.6.4.An example of two dimensional appearance of fine structure in temperature
(top) and density (bottom) taken from the Baltic Sea
Mechanisms of finestructure generation
Thermohaline finestructure can be generated by
• turbulent mixing;
• convective mixing due to double diffusion and/or cabbeling;
• kinematic effect of internal waves;
• interleaving (intrusive layering in oceanic fronts);
Two main types of thermohaline finestructure
Let us consider linear vertical profiles of temperature, salinity and density
T ( z) = T0 + Tz z , S ( z) = S0 + S z z , ρ / ρ 0 = 1 − α (T − T0 ) + β( S − S 0 )
(6.1)
Lecture on Oceanography by Victor Zhurbas
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where α , β are the thermal expansion and salinity contraction coefficients,
ρ z / ρ 0 = −αTz + βS z < 0 , the z axis is upward. If we consider an mixing event in a layer of
thickness h, this event will create a finestructure fluctuation of temperature T ′ , salinity S ′ and
density ρ ′
(6.2)
T ′ ≈ hTz , S ′ ≈ hS z , ρ ′ ≈ hρ z
so we will have for the ratio of temperature/salinity/density fluctuation
v
(6.3)
T ′: S ′: ρ ′ = Tz : S z : ρ z
We may expect that (6.3) is valid for finestructure generated by any kind of vertical
mixing and as well as by straining/pinching of vertical profiles due to internal waves. This type
of finestructure is free of inversions.
Thermohaline finestructure that obeys (6.3) and is free
of inversions is called the step-like finestructure.
Let us consider a pure thermohaline front with vertical profiles (6.1) in one side of it, and
(6.1′)
T ( z) = T0 + Tz z + δT , S ( z) = S0 + Sz z + δS , ρ / ρ 0 = 1 − α (T − T0 ) + β( S − S 0 )
on another side, where δT, and δS are the temperature and salinity jump across the front so that
the density jump vanishes
(6.4)
α * δT = β * δS
If we consider some intrusive, cross-front horizontal motion, this motion will generate
finestructure fluctuation
(6.5)
T ′ ≈ δT , S ′ ≈ δS
so the following relationship will be satisfied
(6.6)
αT ′ ≈ βS ′
It this case, inversions in temperature and salinity are allowed, while the density profile is about
unchanged and remains free of inversions.
Thermohaline finestructure that obeys (6.6) and usually displays temperature
and/or salinity inversions is called the intrusive-like finestructure.
Why in Fig.6.1 we see temperature inversions and no salinity inversions? Why in Fig.6.3
we see salinity inversions and no temperature inversions?
In accordance with (6.6), relative fluctuation of vertical gradient of salinity in intrusivelike finestructure can be presented as
S z′ αTz′ Tz′ αTz Tz′
=
=
= Rρ
(6.7)
S z βS z Tz βS z Tz
αTz
is the mean density ratio which characterizes relative parts of temperature and
βS z
salinity in density stratification. It is clear, that inversions in temperature (salinity) do exist if
| Tz′ / Tz | > 1 ( | S z′ / S z | > 1 ). Therefore, in accordance with (6.7), in the case of strong domination of
temperature in density stratification (i.e., when | Rρ | >> 1 ) it is possible that | Tz′ / Tz | < 1 while
where Rρ =
| S z′ / S z | > 1 , and inversions exist in salinity only. This is just the case of Fig.6.3, where
Rρ ≈ 3 >> 1 . To the contrary, in the case of strong domination of salinity in density stratification
Lecture on Oceanography by Victor Zhurbas
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(i.e., when | Rρ | << 1 ) it is possible that | Tz′ / Tz | > 1 while | S z′ / S z | < 1 , and inversions exist in
temperature only. This is just the case of Fig.6.3, where Rρ ≈ 0.04 << 1 .
Computerized method to determine the type (step-like or intrusive-like) of a finestructure
In order to determine the type of finestructure from CTD data the following method can
be applied.
Suppose that we are considering some vertical profiles of temperature T ( z) and salinity
S ( z) with a specific finestructure. Applying a high-pass filtering to T ( z) and S ( z) we can get
arrays of thermohaline fluctuations Ti ′ and Si′ . Than we may introduce normalized fluctuations
(6.8)
t ′ = αT ′, s ′ = βS ′
and consider a cluster of empirical points ( s ′ , t ′ ) . This cluster will be elongated along some line
that forms an angle ϕ with the s ′ -axis. In terms of principal component analysis, this ϕ gives
the direction of the first eigenvector of the covariance matrix
⎡ s′ 2 s′t ′ ⎤
⎢
⎥
(6.9)
⎢⎣t ′s ′ t ′ 2 ⎥⎦
This ϕ can be calculated as
tan ϕ = p + sign( K ) p 2 + 1, p = (r 2 − 1) / 2 K r
(
where r 2 = t ′ 2 / s′ 2 and K = t ′s′ / t ′ 2 s′ 2
)
(6.10)
1/ 2
.
It is clear from (6.3) and (6.6) that ϕ = 1 in the case of purely intrusive-like structure and
ϕ = Rρ in the case of purely step-like structure.
Than, we may introduce on the plane ( s ′ , t ′ ) two additional angles, ϕ I and ϕ S , defined
as
tan ϕ I = 1, tan ϕ S = Rρ
(6.11)
To avoid ambiguity, we supplement (6.10) and (6.11) by additional constraint
(6.12)
ϕ I = 45o ,−90o < ϕ S − ϕ I ≤ 90o ,−90o < ϕ − (ϕ I + ϕ S ) / 2 ≤ 90o
We now define the parameter δ by which we propose to distinguish step-like and
intrusive-like finestructure:
(6.13)
δ = (ϕ − ϕ I ) / ( ϕ S − ϕ I )
In accordance with (6.11), for purely step-like structure δ = 1 , whereas for purely
intrusive-like structure δ = 0 .
To show the advantage of using definition (6.13), let us consider a simple model of
finestructure in which fluctuations in t ′ and s ′ are represented as superposition of uncorrelated
step-like terms ( sS′ and t S′ ), intrusive-like terms ( s I′ and t I′ ), and an isotropic noise ( sn′ and t n′ )
(6.14)
s ′ = sS′ + sI′ + sn′ , t ′ = t S′ + t I′ + t n′
where the terms on the right side of equations (6.14) satisfy the conditions
sI′ = t I′ , sS′ = t S′ / Rρ , sn′ 2 = t n′ 2 , sI′ sS′ = 0,
(6.15)
sI′ sn′ = 0, sS′ sn′ = 0, sI′ t n′ = 0, sS′ t n′ = 0, sn′ t n′ = 0
Let as denote the ratio of intrusive-like structure variance to step-like structure variance
as
Lecture on Oceanography by Victor Zhurbas
δ IS =
sI′ 2 + t I′ 2
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(6.16)
sS′ 2 + t S′ 2
It can be shown (we do not do it here for brevity) that if δ IS > 1 / 2 ( δ IS < 1 / 2 ), the value
of δ will satisfy the inequality δ < 1 / 2 ( δ > 1 / 2 ) for any values of Rρ and sn′ 2 . Therefore, we
arrive at the following criterion to distinguish mostly intrusive-like structure from mostly steplike structure
δ < 1 / 2 - mostly intrusive-like structure;
δ > 1 / 2 - mostly step-like structure
Next two figures demonstrate the efficiency of utilizing the above criterion to recognize
the type of finestructure.
Fig.6.5. Example of step-like finestructure taken from NE Tropical
.
Atlantic. In this case, δ = 083
Lecture on Oceanography by Victor Zhurbas
Fig.6.6. Example of intrusive-like structure taken from NE Tropical
Atlantic. In this case, δ = 0.042
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