Download Visser 4 Plume

What happens to detritus ?
Fecal pellets
Marine snow
Sinking through water column
Remineralization
How fast
Where
To what extent
Marine snow aggregates
Recycling of nutrients
Sequestering of carbon
…
5 mm
Photo: Alice Alldredge
Organisms associated with detritus
Rich resource
Bacteria
Ciliates
Dinoflagellates
Copepods
Larval fish
colonizers
visitors
gulp
What mechanisms bring about contact?
Plume of released solutes
Photo: Alice Alldredge
Following a chemical trail
First demonstration:
The shrimp Segestes acetes
following an amino acid trail
generated by a sinking
wad of cotton that was
soaked in a solution of
fluorocein and
dissolved amino acids.
Hamner & Hamner 1977
Copepods detect and track chemical plume
Temora
Kiørboe 2001
Physics of small organisms in a fluid: advection - diffusion
C
 uC  D 2 C  0
t
advection
diffusion
ua
Pe 
D
Pe < 1: diffusion dominates
Pe > 1: advection dominates
Heuristic
says nothing about
flux
Plume associated with marine snow
Re = 1 to 10
Pe ≈ 1000
Mate tracking
Centropages typicus: pheromone trail
17 cm long: 30 sec old
Espen Bagoien
Physical parameters for plume encounter
The particle:
The organism:
The medium:
Sinking rate (w, cm/s)
Leakage rate (L, mol/s)
Detection ability – threshold (C* mol/cm3)
Swimming speed (v, cm/s)
Turbulence (e cm2/s3, + ….)
Diffusion (D, cm2/s)
*****
w
What are relevant plume charcteristics ?
Approach: analytic and numerical modelling.
Particle size dependent properties
Sinking rate: w  ar b
Stokes' law
2 g  2
w
r
9
Empirical observations
Marine snow:
a = 0.13, b = 0.26
Fecal pellets:
a = 2656, b = 2
Leakage rate: L  cr d
Empirical observations
(particle specific leakage rate & size
dependent organic matter content)
c = 10-12, d = 1.5
Detection threshold
Species and compound specific
Typical free amino acid concentration: 3 10-11 mol cm-3
specific amino acid concentrations < than this
Copepod behavioural response (e.g. swarming): 10-11 mol cm-3
Copepod neural response: 10-12 mol cm-3
C* from 2 10-12 to 5 10-11 mol cm-3
Zero turbulence
Z 0* 
L
4 DC *
Z 0*
L
T 

w 4 DwC *
*
0
w
Length of the plume
Time for which plume
element remains
detectable
For marine snow r = 0.5 cm and detection
threshold C* = 310-11 mol/cm3
Z0* = 100 cm
T0* = 900 sec
V0* = 2.5 cm3 (5particle)
s0* = 16 cm2 (20 particle)
Jackson & Kiørboe 2004
Effect of turbulence on plume
Straining and Stretching:
Elongates plume lenght
Turbulent
shear event
Increases concentration
gradients – molecular
diffusion faster
Nonuniform: gaps along
plume length
w
w+v
Visser & Jackson 2004
Modelling turbulence
Direct numerical simulations: solve the Navier Stokes equations
Very accurate
Hugely expensive
Large eddy simulations: solve the Navier Stokes equations
for a limited number of scales
Relatively accurate
Hugely expensive
Kinematic simulations: analytic expressions that generate
turbulence like chaotic stirring
Easily done
9
u  C 
5
E(k)
energy density spectrum, E(k)
(L3/T2)
Remember: Kolmogorov spectra theory

1
3
e 2/3
2/3
k5/3
viscous
sub-range
2/Le
2/
wave number, k (2/ℓ)
inertial
sub-range
k
Governed by 2 parameters
viscosity n
dissipation rate e
Synthetic turbulence simulations
k1
E(k)
k2
kN
k5/3
E(k )  E0k 5 / 3
viscous
sub-range
2/Le
2/
inertial
sub-range
k
N
u(x, t )  
n 1
 a  kˆ cosk
b  kˆ sin k
n
n
n
 x   nt  
n
n
n
 x   nt 
E(k)
Synthetic turbulence simulations

Assumed energy spectrum:
E (k )  E0k 5 / 3
frequency:
n  e 1/ 3k 5 / 3
k̂ n
an , bn
viscous
sub-range
2/Le
Wave number, k, ranges from kmin to kmax
Amplitude of Fourier
coefficients:
k5/3
2/
k
inertial
sub-range
an  bn  2E(kn )dkn
2
2
Random unit vector in 3 D: k n  k kˆ n
Random 3 D vectors of magnitude an and bn respectively
Fung, 1996. J Geophys Res
Simulation
Particle
Path of sinking particle
Plume
Path of a neutrally
plume tracer
Particle tracking
by Runge-Kutta
integration
Plume concentration
Gaussian
distribution
of solute
C
f

ℓ
C*
Plume
 *

Plume construct: stretching and diffusing
stretching
 2 
f i  Ci exp  2 
 i 
2


fis1  Ci exp   2
  s
 i i, j
si , j 




diffusing
2
2



C

d
i
i
f i1 
exp 
2
2
4 D   i
 4 D   i 
i, j
i 1, j

2
fi 1 
exp  
2
 4 D   2 s
4 D  i si , j
i i, j

i 2Ci si , j

 2 
  Ci 1 exp   2 

 i 1 

Mesopelagic (10-8 cm2/s3)
Marine snow: r = 0.1 cm
w = 0.07 cm/s (60 m/day)
Themocline (10-6 cm2/s3)
Marine snow: r = 0.1 cm
w = 0.07 cm/s (60 m/day)
Surface (weak) (10-4 cm2/s3)
Marine snow: r = 0.1 cm
w = 0.07 cm/s (60 m/day)
Surface (strong) (10-2 cm2/s3)
Marine snow: r = 0.1 cm
w = 0.07 cm/s (60 m/day)
Model runs
10 levels of turbulence
3 particle sizes each for marine snow and fecal pellets
4 replicates for each turbulence – size pairing
3 detection threshold
Metrics of interest
Length; cross-sectional area; degree of fragmentation
Natural time scales:
turbulence: g = (n / e)1/2 or 1 / mean rate of strain
plume: T0* time scale for plume element to drop below threshold of
detection.
Metric scale:
nonturbulent values
Total Volume
1.2
Marine snow
1.0
V* / V0*
0.8
Symbols: different detection threshold
Colour: different particle size
0.6
0.4
e 
g  
n 
1/ 2
0.2
0.0
10-4 10-3 10-2 10-1 100
101
102
103
104
105
g T0 *
Fit:
*
V
0
V* 
1  0.25g T0*
106
Rate of turbulent straining
Rate of diffusion
p < 0.0001
Visser & Jackson 2004
Total Cross section
1.2
Marine snow
1.0
s* / s 0 *
0.8
0.6
0.4
0.2
0.0
10-4 10-3 10-2 10-1 100
101
102
103
104
105
106
g T0 *
Fit:
*
s
0
s* 
1  0.1g T0*
p < 0.0001
Visser & Jackson 2004
1st Segment Length (distance following plume)
1.2
Marine snow
1.0
Z 1 * / Z0 *
0.8
0.6
0.4
0.2
0.0
10-4
10-3
10-2
10-1
100
101
102
103
104
105
g T0 *
Fit:
*
1

0.4
g
T
0
Z1*  Z 0*
1  0.8g T0*
p < 0.0001
106
What can we use this for
Copepod encounter with appendicularian houses
Appendicularia
Copepods
Microsetella
(harpacticoida)
0.7 mm
Oncaea
(cyclopoida)
Fritillaria
borealis
Oncaea borealis
Microsetella norvegica
Oikopleura
dioica
5 mm
Oncaea similis
Remember: Ballistic model variations
Z  CR u
2
Z  C (s  b)u
b
s
u
s
10
s0
1  0.1gT0
e 
g  
n 
2
Cross section (cm )
1/ 2
1
0.1
L
T0 
4DwC *
10 m d-1
20
50
100
200
0.01
10-10 10-9 10-8 10-7 10-6 10-5 10-4
e (m2 s-3)
0.24  L 
s0 
1/ 2 
* 
Dw  C 
3/ 2
w(cm/s )  0.13a(cm)
0.26
C* = 3 10-8 µM
L = 9 10-14 mol s-1
Maar, Visser, Nielsen, Stips & Saito. accepted
-1
Clearance rate (cm s )
0.35
3
0.30
0.25
  vs  2b
0.20
0.15
v = 0.1 cm s-1
0.10
b = 100 µ
0.05
0.00
10-10
w = 10 m day-1
10-9
10-8
10-7
10-6
10-5
10-4
Dissipation rate (m2 s-3)
Maar, Visser, Nielsen, Stips & Saito. accepted
Copepod encounter with appendicularian houses
surface
(above 20 m depth) 0.6 per day per copepod
2.5 per day per appedicularian house
e =10-2 cm2/s3
g= 1 s-1
10% per day
10 m day-1
Chouse = 244 m-3 below 30 m
Ccopepod = 1000 m-3
below thermocline
(below 30m depth)
e =10-7 cm2/s3
g= 10-3 s-1
4.4 per day per copepod
18 per day per appedicularian house
50% per day
Microsetella norwegica
Depth of centre of mass (m)
0
Skagerrak spring
Skagerrak summer
The North Sea
20
r2=0.73
p<0.05
40
r2=0.59
p<0.01
60
80
-8
-7
-6
-5
-4
-3
log10 surface dissipation rate (m2 s-3)
Maar, Visser, Nielsen, Stips & Saito. accepted
Summary remarks
Despite complexity there seem to be global functions relating plume metrics
in turbulent and non-turbulent flows.
About 50% of the detectable signal becomes disassociated from the particle
in high turbulence.
Significant advantages can be had for chemosensitive organisms searching
for detrital material in low turbulent zones (below the thermocline).
Aspects turbulence and its effects on mate finding still to be explored
Encounter rate is everything to plankton
How to
Find food
Find mates
Avoid predators
Relative motion
Sensing ability
Turbulence
Encounter processes
Random walks link
microscopic (individual)
behaviour with macroscopic
(population) phenomena
Random walk - diffusion
Ballistic - Diffusive
Scale of interactions
Ingestion rate
Encounter rate and turbulence: Dome - shape
turbulence
Patchiness
Simple population models + chaotic stirring → complex spatial patterns