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Physics of small organisms in fluids. Chemical plumes. What happens to detritus ?. Fecal pellets Marine snow. Sinking through water column. Remineralization. Marine snow aggregates. How fast Where To what extent. Recycling of nutrients. Sequestering of carbon. …. 5 mm.

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Physics of small organisms

in fluids

Chemical plumes


What happens to detritus ?

Fecal pellets

Marine snow

Sinking through water column

Remineralization

Marine snow aggregates

How fast

Where

To what extent

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



Physics of small organisms in a fluid: advection - diffusion

advection

diffusion

Pe < 1: diffusion dominates

Heuristic

says nothing about flux

Pe > 1: advection dominates


Plume associated with marine snow

Re = 1 to 10

Pe≈ 1000



Centropages typicus: pheromone trail

17 cm long: 30 sec old

Espen Bagoien


Sinking rate (w, cm/s)

Leakage rate (L, mol/s)

The particle:

Detection ability – threshold (C* mol/cm3)

Swimming speed (v, cm/s)

The organism:

Turbulence (e cm2/s3, + ….)

Diffusion (D, cm2/s)

*****

The medium:

w

Physical parameters for plume encounter

What are relevant plume charcteristics ?

Approach: analytic and numerical modelling.


Particle size dependent properties

Sinking rate:

Stokes' law

Empirical observations

Marine snow:

a = 0.13, b = 0.26

Fecal pellets:

a = 2656, b = 2

Leakage rate:

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* from2 10-12 to 5 10-11 mol cm-3


Zero turbulence

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)

w

Jackson & Kiørboe 2004


Effect of turbulence on plume

Straining and Stretching:

Elongates plume lenght

1

Increases concentration gradients – molecular diffusion faster

2

Turbulent

shear event

Nonuniform: gaps along plume length

3

w + v

w

Visser & Jackson 2004


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

Modelling turbulence

Kinematic simulations: analytic expressions that generate turbulence like chaotic stirring

Easily done


Remember: Kolmogorov spectra theory equations

energy density spectrum, E(k) (L3/T2)

Governed by 2 parameters

viscosity n

dissipation rate e

wave number, k (2p/ℓ)


Synthetic turbulence simulations equations

+ ..... +

+

k1

k2

kN


Synthetic turbulence simulations equations

Wave number, k, ranges from kmin to kmax

Assumed energy spectrum:

frequency:

Amplitude of Fourier

coefficients:

Random unit vector in 3 D:

Random 3 D vectors of magnitude an and bn respectively

Fung, 1996. J Geophys Res


Path of sinking particle equations

Plume

Path of a neutrally plume tracer

Particle tracking by Runge-Kutta integration

Simulation

Particle


Plume equations

Plume concentration

Gaussian distribution of solute

C

f

r

C*

r*

l

r


stretching equations

diffusing

Plume construct: stretching and diffusing


Mesopelagic (10 equations-8 cm2/s3)

Marine snow: r = 0.1 cm

w = 0.07 cm/s (60 m/day)


Themocline (10 equations-6 cm2/s3)

Marine snow: r = 0.1 cm

w = 0.07 cm/s (60 m/day)


Surface equations(weak) (10-4 cm2/s3)

Marine snow: r = 0.1 cm

w = 0.07 cm/s (60 m/day)


Surface equations(strong) (10-2 cm2/s3)

Marine snow: r = 0.1 cm

w = 0.07 cm/s (60 m/day)


Model runs equations

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 equations

Symbols: different detection threshold

Colour: different particle size

Rate of turbulent straining

Rate of diffusion

Fit:

p < 0.0001

Visser & Jackson 2004


Total Cross section equations

Fit:

p < 0.0001

Visser & Jackson 2004


1 equationsst Segment Length (distance following plume)

Fit:

p < 0.0001



Copepod encounter with appendicularian houses equations

Appendicularia

Copepods

Oncaea

(cyclopoida)

Microsetella

(harpacticoida)

0.7 mm

Fritillaria

borealis

Oncaea borealis

Microsetella norvegica

Oikopleura

dioica

5 mm

Oncaea similis



b equations

s

u


C equations* = 3 10-8 µM

L = 9 10-14 mol s-1

Maar, Visser, Nielsen, Stips & Saito. accepted


v equations = 0.1 cm s-1

b = 100 µ

w = 10 m day-1

Maar, Visser, Nielsen, Stips & Saito. accepted


Copepod encounter with appendicularian houses equations

  • surface

  • (above 20 m depth)

  • =10-2 cm2/s3

    g = 1 s-1

0.6 per day per copepod

2.5 per day per appedicularian house

10% per day

10 m day-1

Chouse = 244 m-3 below 30 m

5x

Ccopepod = 1000 m-3

  • below thermocline

  • (below 30m depth)

  • =10-7 cm2/s3

    g = 10-3 s-1

4.4 per day per copepod

18 per day per appedicularian house

50% per day



Summary remarks equations

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


Relative motion equations

Sensing ability

Turbulence

1

Encounter rate is everything to plankton

Find food

Find mates

Avoid predators

How to


2 equations

Encounter processes

Random walks link microscopic (individual) behaviour with macroscopic (population) phenomena

Random walk - diffusion

Ballistic - Diffusive

Scale of interactions


Ingestion rate equations

turbulence

3

Encounter rate and turbulence: Dome - shape


4 equations

Patchiness

Simple population models + chaotic stirring → complex spatial patterns


Thanks equations


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