Environmental Fluid Mechanics –
Hydropower Plants
(a.y. 2012/13, 9 credits – 90 hours)
Transport processes and impacts
Marco Toffolon
e-mail: marco.toffolon@ing.unitn.it
Laboratorio Didattico
di Modellistica Idrodinamica
(2nd floor, central corridor)
tel.: 0461 28 2480
Hydrology and water resources
Constructions
e-mail: alberto.bellin@ing.unitn.it
e-mail: maurizio.righetti@ing.unitn.it
prof. Alberto Bellin
prof. Maurizio Righetti
Part II: Transport processes in the environment
II-1. Introduction (10 hours)
Basic concepts: definition of concentration, mass balance, diffusion. Turbulent mixing. Gaussian
model for diffusion processes: basic solution and typical scales. Advection-diffusion equation
and analytical solutions in the one-dimensional context. Phases of mixing: near field,
intermediate field, far field. Dispersion resulting from non-uniform advection. Dynamics of
reactive tracers (including temperature): zero- and one-dimensional models.
II-2. Transport processes in rivers and effects of hydropower production (9 hours)
Review of basic hydraulic concepts. Estimates of turbulent diffusion and dispersion coefficients.
Flood waves due to sudden releases from hydropower plants (hydropeaking). Temperature
waves due to the temperature differences between rivers and hydropower releases
(thermopeaking). Introduction to river morphology. Hints on biological effects of hydro- and
thermo-peaking. Modification of habitats in impacted rivers. Numerical models for longitudinal
dispersion: examples.
II-3. Thermal dynamics of reservoirs (9 hours)
Heat budget in closed basins. Stratification cycle and implications on vertical mixing. Effect of
withdrawals and inflows on the temperature profile. Hints on biological aspects and water
quality. Numerical models for hydro-thermodynamics of reservoirs: examples. Application to a
real case: reservoir management and impact on downstream river.
~28 hours
Main references
Lecture notes.
Suggested textbook (transport processes):
S.A. Socolofsky & G.H. Jirka, dispense del corso Special Topics on Mixing and Transport in the
Environment, Texas A&M University, 2005.
link on website: http://www.ing.unitn.it/~toffolon/ (“Materiale didattico”)
Further reading on environmental fluid mechanics:
Fischer H.B., Koh J., List J., Imberger J., Brooks H., Mixing in Inland and Coastal Waters, Academic
Press, New York, 1988.
Rutherford J.C., River Mixing, John Wiley & Sons, Chichester, 1994.
J.L. Martin, S.C. McCutcheon, Hydrodynamic and transport for water quality modeling, Lewis Publishers
CRC Press
About HP impacts on the environment:
Journal papers
Environmental fluid
mechanics:
An emblematic case
Deepwater Horizon
oil spill
http://earthobservatory.nasa.gov/NaturalHazards/event.php?id=43733
21/04/2010
http://fastfreenews.com/wp-content/uploads/2010/06/gulf-oil-spill1.jpg
25/04/2010
01/05/2010
09/05/2010
17/05/2010
24/05/2010
12/06/2010
19/06/2010
Impacts of hydropower production
Thermal structure
Reservoirs
Rivers
Ecosystems
Sediments
Macro-benthos
Fishes
Infilling
Clogging
Coasts
Eco-hydraulics in Trento: a multi-disciplinary research group
Department of Civil and Environmental Engineering
University of Trento, Italy
Bruno Maiolini
M. Cristina Bruno
Nunzio Siviglia
Guido Zolezzi
Hydropeaking: qualitative description
Typical medium-term
behaviour:
daily cycle + weekly cycle
due to the production of
peaks of electricity.
Sunday
Saturday
Friday
Thursday
Wednesday
Tuesday
Monday
Simplifying assumption:
waves have approximately a
square shape.
Sunday
Stage variations are very rapid
(order of cm/min or m/h)
both in the rising and in the
decreasing phase
 travelling waves.
… and what is thermopeaking?
temperature of reservoir
≠
temperature of river
http://www.racine.ra.it/europa/uno/esame2003/terzaf/vcv/html/due.htm
Hydropeaking  thermal alteration
Intensity changes during the year
Main concepts
Transport in the environment
passive tracer
C
concentration:
M
V
flow field
1
1. mass is conserved
3
2
(non-reactive tracers)
2. concentration tends to become
spatially homogeneous
dM
0
dt
(exceptions:
reactive tracer 
oxygen, nutrients,
and temperature)
“diffusion”
Diffusion
Diffusive flux works against
concentration gradient
  DC
Fick law
(1855)
Phenomenological explanation:
random displacement rightward or leftward
N steps (time)
200 “balls”, probability of movement 0.2, single boxes
Main features of diffusive processes
Characteristic dimension of the cloud
L(t )  Dt
1
L(t1)
2
L(t2)
Self-similar Gaussian solution
3
L(t3)
(1D, infinite domain)
 x   2 

C1D x  
exp 
2

2
2 2


M
with variance
 2  2Dt
“mass” between
extreme points:
±  68.3%
±2  95.5%
±3  99.7%
How an advective process becomes diffusive…
Molecular diffusion
(property of tracer+fluid)
Thermal oscillations
typical values in water ~ 10-5 cm2/s = 10-9 m2/s
in air ~ 10-5 m2/s
Turbulence (“random” advection)
Turbulent diffusion
(property of the flow field,
and not of the tracer+fluid)
for times long enough
(longer than the integral scals of turbulence)
Non-uniform
advective motion
+ diffusion
orthogonal to the flow
Dispersion
(combined mechanism)
for times long enough
(longer than the characteristic scale of orthogonal diffusion)
Dispersion:
phenomenological description
y
u(y)
non-uniform
advective motion
 cloud
distortion along x
orthogonal
diffusion
 “compacts”
the cloud along y
dispersion
 enhanced
“diffusion” along x
x
Lagrangian model: following particles
deterministic component
(assigned flow field)
random component
(turbulence or thermal oscillation)
Numerical simulation
concentration C(x)
zoom
C(y)
zoom
y
particles
y
x
particles in the x,y domain
x
River mixing
B
hp. shallow water, large width (B>>Y)
z
Y
vertical mixing is much faster than
transverse mixing
y
Mixing phases
source
near field: 3D model, turbulent diffusion
(+ molecular)
completed vertical mixing
intermediate field: 2D model (depth-averaged),
dispersion + turbulent diffusion (+ molecular)
completed transverse mixing
far field: 1D model (cross-section-averaged), dispersion
(+ turbulent diffusion + molecular)
Gallery of images
Point source in a river 1/2
flow direction
Tracciante rilasciato in un fiume. Il mescolamento verticale viene
raggiunto molto velocemente (a distanza di circa 10 volte la
profondità); il mescolamento trasversale è molto più lento.
Point source in a river 2/2
Le curve incrementano fortemente il mescolamento trasversale a
causa delle correnti secondarie.
Confluence
Confluenza di tre fiumi: a sinistra, con una concentrazione molto alta
di particolato; al centro con una concentrazione intermedia; a destra
(più scuro), più pulito. Contorni ben definiti separano di diversi flussi.
[Inn a sinistra, Danubio al centro, Passau DE]
Un caso concreto: Scarico accidentale in un corso d’acqua
Fasi del problema
rio Sorne
fiume Adige
scarico massa M
fase 1:
mixing nel rio Sorne
fase 2:
confluenza
fase 3:
mixing nell’Adige
fase 4:
cosa succede a valle?