Transport in Aquatic Ecosystems

Horizontal Inflows - Advection

Turbulence – critical for vertical fluxes

Turbulent Eddies

These Play a Key Role in Vertical and Horizontal Transport!!!

Dimensionless Numbers

• Comprehensive terms that take into account all the variables influencing the potential for a type of flow

• Reynolds Number

• Richardson Number

• Wedderburn Number

Re and Ri are used to determine whether flows will become turbulent.

W is used to determine whether wind forcing will induce tilting of the thermocline and ultimately shear production and turbulence.

Reynolds Number - Re

• Re = u l/ vu = velocityl = a linear dimension (e.g., width of a pipe, depth of the mixed layerLength of a submerged coral reef)V = kinematic viscosity (a measure of the stickiness of a fluid) 10-6 m2 s-1

Ratio of the inertial forces that set a fluid in motion to the viscous ones that retard motion.

Indicates whether a flow will be laminar or turbulent.

High values indicate turbulence!

Applies to unstratified flows and flows around organisms.

Laminar and Turbulent Flows

Turbulent Boundary Layer

Can be driven by heat loss at air-water interface and/or shear.Upper photos, Reynolds Number = 9400, lower, 600.

Wind Induced Circulation in Lakes

Mortimer

Entrainment and Mixed Layer Deepening

Occurs due to heat loss generally in combination with wind forcing.

Examples: Sargasso Sea during Fall and Winter Mono Lake during Fall and Winter L. Victoria during Monsoon period Nocturnal cooling

Z

Temperature

Temperature, Summer in AM(note, mixed layer will stratify in Afternoon unless it is cloudy).

Temperature after cooling,Mixed layer is deeper and cooler.

If nutrient concentrations are higher at the depths where waterIs entrained than in the overlying water, these events will lead to increased concentrations in the overlying water.

Turbulence in Upper Mixed Layer

• Circulates phytoplankton cells • May reduce photoinhibition leading to higher

overall rates of photosynthesis

• May facilitate or reduce success of feeding by zooplankton and fish larvae.

• May entrain nutrients from thermocline

Internal Waves in Stratified Flows

Initiated by wind.

Shear Flow induces Stretching of Patches

Shear is induced by currents from wind or internal waves.

Richardson Number - RiRatio of buoyancy forces to inertial forces.

Ri = g/p (dp/dz)/(du/dz)2

g = gravity (9.81 m s-2)p = density (kg/m3)z = depthu = velocity

Instability results if Richardson number drops below critical value.Ri < 0.25

Applies to stratified flows!

Kelvin Helmholtz Billows

Form due to shear in Stratified water bodies

Instability results ifRichardson numberdrops below critical value.

Ri < 0.25

Ri = g/p (dp/dz)/(du/dz)2

g = gravity (9.81 m s-2)p = density (kg/m3)z = depthu = velocity

Tracer Experiments in Mediterranean Sea

Do Kelvin Helmholtz BillowsOccur in Nature?

Kelvin Helmholtz Billows

Vertical and Horizontal Scales – 10 m and 100 m respectively.

Frequency of Billows in Loch Ness

Frequency of density inversions:

Black ~30%

Dotted 15-30%

Gray < 15%

White – not detected.

Wind Induced Circulation

• 3 dimensional model of hydrodynamics of Lake Kinneret, Israel.

Where Does Turbulence Occur?

Throughout metalimnion?

Near Boundaries???

With subsequent flows to interior?

Dimensionless Indices – Wedderburn Number

• Indicates whether wind forcing is sufficient relative to stratification to induce shear to mix a lake.

• W = (g (dp/dz) h2 ) / pu*2L

g = gravity (9.8 m s-2)p is density (kg m-3)h is mixed layer depthu* is water friction velocity, 0.001 times wind speedL is length of the lake

U U

U U

W > 152 < W < 15

W ~ 1 W << 1

No shear Shear

Shear

Completemixing

EddiesRi > 0.25Kz, molecular

Ri < 0.25 occasionallyKz > molecular

Ri < 0.25 more frequentlyKz > 10 to 100 x molecular diffusivity

thermocline

Wedderburn Number and extent of Mixing in Metalimnion

Thermocline, before wind

Thermocline tilt from wind

3 D Hydrodynamic Models of Internal Waves for different values

of Wedderburn Number

Where will Fluxes of Nutrients Occur?

Mid-lake?

At a Lake’s Boundaries

If Nutrient Fluxes are Spatially Heterogenous, What will be the Impact on Primary Production?