Sensing ability

Find foodFind matesAvoid predators

Encounter rate is everything to plankton

How to

Relative motion

Turbulence

Encounter rate is everything for plankton

understanding the mechanisms of individual organisms interacting

motion diffusion

challenging

gives a deeper understanding of macro-scale effects

why?

Microscopic

Mechanistic

Individual

Macroscopic

Empirical

Population

Individual based models

How individuals

move

interact with environment

interact with each other

The particle nature of organisms

The physics of small particles in a fluid

Hydrodynamics: how small orgamisms move and the flow associated with them

Diffusion: how material is exchanged with small orgamisms.

At scales that do not lead to immediate intuition

Viscosity is all important

How important is determined by the Reynolds number

uaRe

a is the size (radius say) of the particleu is the speed at which it is moving relative to the fluid is the kinematic viscosity of the fluid

forces viscous

forces inertialRe

Physics of small organisms in a fluid: hydrodynamics

Note: kinematic viscosity , dynamic viscosity

dimensions L2 T1 dimensions M L1 T1

≈ 10-2 cm2 s-1 for water

Re < 1: vicosity dominates, Stokes' regimeRe > 1: inertia becomes importantRe > 2000: flow becomes turbulent

Typical valuesswimming bacterium 10-5

swimming flagellate 10-3

copepod feeding current 1

Physics of small organisms in a fluid: hydrodynamics

fuvguv

22

9

aDt

D

dt

d ffpfp

particle acceleration

local fluidacceleration (pressure gradient)

buoyancy drag self induced force

f

p

Settling velocity (Stokes' law)

02

92

wa

g ffp

radius a

f

fpgaw

9

2 2

marine snow (1 mm) 6 m/day

vu

Physics of small organisms in a fluid: hydrodynamics

Physics of small organisms in a fluid: hydrodynamics

-4 -3 -2 -1 0 1 2 3 4-4

-3

-2

-1

0

1

2

3

4

U

r

3

3

22

31cos

r

c

r

aUur

3

3

44

31sin

r

a

r

aUu

Stokes' flow around a sphere

Effected volume>> then particle

Diffusion of solutes:nutrientswaste products (oxygen)

Diffusivity (D) of many solutes(salt, sugar, O2, nitrate)D ≈ 10-5 cm2/s

04 CCaDQ OsmotrophInward flux

02

3

* 3

34

CCDaa

QQ

VolumeSpecific flux

Becomes less efficient for larger organism

Steady state

Physics of small organisms in a fluid: diffusion

Dt

aCCaDtQ

14)( 0

time dependent flux to a sphereQ

t

Physics of small organisms in a fluid: diffusion

So why not just jump form place to place ?

02

CDCut

C

advection diffusion

D

uaPe

Physics of small organisms in a fluid: advection - diffusion

Pe < 1: diffusion dominates

Pe > 1: advection dominates

Heuristic

says nothing about flux

0 4 CCShaDQ

Physics of small organisms in a fluid: advection - diffusion

diffusive

total

Q

QSh

Calculate using model: solve 02

CDCut

C

Sherwood number

-5 0 5-5

0

5Stokes' flow

Str

ea

mlin

es

-5 0 5-5

0

5

Ve

loci

tyR

ad

ial d

ista

nce

fro

m c

en

ter

( a)

0.9

-5 0 5-5

0

5

Vo

rtic

ity

0.1

-5 0 5-5

0

5 Re=1

-5 0 5-5

0

5

0.9

-5 0 5-5

0

5

Radial distance from center (a)

0.1

-5 0 5-5

0

5 Re=10

-5 0 5-5

0

5

-5 0 5-5

0

5

1.0

0.1

Step 1: calculate the flow

Step 2: solve for a solute.

Physics of small organisms in a fluid: advection - diffusion

Agar sphere filled with oxygen consuming yeast cellsSuspended in flow (= sinking)

Physics of small organisms in a fluid: advection - diffusion

Re

0 5 10 15 20 25

Sh

erw

ood

num

ber

0

5

10

15

20

25

30

Numerical result

08.03/162.01 RePeSh

2/)21(1 3/1PeSh

Empirical

Physics of small organisms in a fluid: advection - diffusion

Thoretical

0.5 µ bacteria, u = 2 10-5 cm/s, Re = 10-7, Pe = 10-4, Sh = 1.00

5 µ flagellate, u = 3 10-4 cm/s, Re = 10-5, Pe = 10-2, Sh = 1.01

Where advection (swimming, sinking etc) doesn't matter

500 µ algal colony, u = 7 10-2 cm/s, Re = 0.4, Pe = 400, Sh = 5

1 mm marine snow, u = 7 10-2 cm/s, Re = 1, Pe = 700, Sh = 6

1 cm marine snow, u = 0.13 cm/s, Re = 13, Pe = 1300, Sh = 19

and where it does

Physics of small particles in a fluid: advection - diffusion

Acartia tonsa nauplii

Jumps 3 times per second.Why?

a few 100 µ in size

Hydromechanical signals in the plankton

Many blind plankton organisms, from the smallest flagellates to crustaceans, are capable of perceiving and identifying moving objects - prey, predator, mate – and to react adequately.

Ciliates entrained into the feeding current of Temora

Sensory ability of copepods

Sensory ability of copepods

40 m

200 m

Labidocera madurae

5 m

Mechano-receptive setae are velocity detectors

Neurological sensitivity 20 m / s

Sensory ability of copepods: Acatia tonsa

Siphon flow longitudinal deformation acceleration

Oscillating chamber acceleration

Couette device shear deformation acceleration vorticity

Rotating cylinder acceleration vorticity

Acartia tonsa150 m / s

Velocity difference

rate of strain(deformation)

-4 -3 -2 -1 0 1 2 3 4-4

-3

-2

-1

0

1

2

3

4

-4 -3 -2 -1 0 1 2 3 4-4

-3

-2

-1

0

1

2

3

4

U

U

Translating sphere Spherical pump

sinking particle feeding current

2 models for the price of one

Small prey entrained into a copepod feeding current

3

3

22

3cos

r

c

r

aUur

3

3

44

3sin

r

a

r

aUu

Small prey entrained into a copepod feeding current

Translation Deformation

Translation

Rotation

Deformation

(b) Across flow velocity gradient: Simple shear flow

(a) Along flow velocity gradient

Small prey entrained into a copepod feeding current

Small prey entrained into a copepod feeding current

)2/()(3)( 422 rarUar

Peak: 0)(

r

r

a

Ur

ar

8

3*)(

2*

Because typically swimming velcity (U) scales with size (a)maximum deformation rate is approximately constant and size independent

Deformation rate

Distance, units of a

0 5 10 15 20 25

Def

orm

atio

n ra

te (

units

U/a

)

0.0

0.2

0.4 = 0o

Small prey entrained into a copepod feeding current

Reaction distance

)2/()(3)( 422 rarUar

To find R, solve for r = R at ∆(r) = ∆*

U

a

a

UaR

3

*811

*4

3

Reaction distance function of size and velocity

Distance (units of a)

0 5 10 15 20 25

De

form

atio

n ra

te (

uni

ts U

/a)

0.0

0.2

0.4

R

Small prey entrained into a copepod feeding current

Data taken from Tiselus & Jonsson 1991

Distance, cm

0.0 0.1 0.2 0.3 0.4D

efo

rma

tion

ra

te,

s-1

0

2

4

6

8

10

12

14

Deformation

Distance, cm

0.0 0.1 0.2 0.3 0.4

Fee

ding

cur

ren

t ve

loci

ty,

cm s

-1

0.2

0.4

0.6

0.8

1.0Observed

Modelled

Centropages feeding current: observed and modelled

Observed reaction distance, cm

0.0 0.1 0.2 0.3 0.4 0.5Pre

dic

ted

rea

ctio

n d

ista

nce

, cm

0.0

0.1

0.2

0.3

0.4

0.5

1

2

3 4

5

1: Stickleback-Temora; 2: Centropages-Acartia nauplii;3: Temora-Acartia nauplii; 4: Stickleback-Eurytemora;5: Larval cod - Acartia nauplii

A small prey is embedded in the flow generated by a large moving predator – hence responds to velocity gradients rather than velocity

Velocity or velocity gradients

A large predator is anchored in the fluid and not moved by the flow generated by a small swimming prey – hence respond to absolute flow velocity

what does he experience

what does he experience

Large predator detecting a particleThere is a fundamental difference between the a body force (gravity and sinking) and a self-prpoelled body (swimming)

drag

buoyancy

drag

thrust

0

0

0 0

STRESSLETSTOKESLET

Velocity

Distance, units a

0 5 10 15 20 25

Abs

olu

te fl

uid

ve

loci

ty (

un

its o

f U)

0

1 = 00

3

3

22

31

r

c

r

aUur

Large predator detecting a particle

Velocity

Distance, units a

0 5 10 15 20 25

Abs

olu

te fl

uid

vel

ocity

(un

its o

f U)

0

1 = 00

3

3

22

31

r

c

r

aUur

Find R at ur = S*

))3/))/*(cos4cos((2/( 1 USaaR

Reaction distance function of size and velocity

R

S*

Large predator detecting a particle: reaction distance

For sinking particle

Similar for swimming organism

Does it work like this?

Acartia percieving sinking fecal pellets

Ambush feeding:remotely perceived prey are attacked

Oithona feeding on motile Gymnodinium

Detection distance = 0.14 mm => S* = 40 µm/s

Oithona percieves small swimming flagellates

Oithona: Predicted and observed clearance rates (S* = 40 m/s)

Fecal pellet equivalent spherical radius, cm

0.001 0.01

Cle

aran

ce, m

l d-1

0.1

1.0

10.0

100.0

1000.0

10000.0

PredictedPredictedAcartia tonsa (lab)Large Calanoids (lab)Large Calanoids (field)

Prey volume, um^3

100 101 102 103 104 105

cle

ara

nce

, m

l /h

0.0

0.2

0.4

0.6Predicted, frontPredicted, sideobserved

Flagellates Sinking faecal pellets

Data from Turner

• Simple, idealised models may provide insights in the basic mechanisms of hydrodynamic signalling in the plankton

• More realistic models are computationally heavy, but may be required to adress specific questions. Such models are now beginning to emerge

• Modelling is fine – but there is no substitute for direct observations

• Physics of small marine organisms are often not intuitive.

• Qualitative insights can be got from nondimensional numbers such as Re, Pe and Sh

Final remarks