Interdisciplinarity
for Natural Sciences
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|
Mathematical
Physics in Surface Hydrology
G.
Vitali
FM60
- December 20 2002
Introduction
FM
Mathematical Physics
- Wave
motion (linear and N.L.)
- Wave
Dispersion and Damping
- Special
Functions
- Anomalous
diffusion
- Stochastic Processes
The
body of Agronomy
' ' ' 
- Agriculture and Agronomy
- Crop
Science and Soil-Plant-Atmosphere-System

Surface
Hydrology
- Landscape
Complexity
- Hydrological
Networks
- Runoff
- Infiltration
- Vadose
- Cultivated Layer

Continnum
Approach and REV
- Unsatured
Darcy-Buckingham / eq. di Richards


- Theoretical
works by Philip - Infiltration
- B.C.s
-
absorption
- infiltration
- redistribution
- capillary
rise
- evaporation
- Transport
of chemicals - ADE
- Adsorbed
reacting chemicals (chromatography)
- Multiple Region

- Parameterization
of Retention
- Pedo
Transfer Models by Mualem - Burudine
Continnum
Approach and REV
- Hydrograph
modelling
- Prediction
from Ungaged Basins (PUB)
- Instant Unit Hydrograph (IUH)

. . . 

Key
Processes
Statement
- Surface
Runoff
- Water
Transport
- Solute
Transport
Soil
as a Complex System
- Complex
System
- Porous
- Granular
- Disordered
- Cemented
- Aggregate
- Factured
- Elastic
- Swelling
- Multi-scale
- SOIL STRUCTURE
- Dynamics - Stability
- Ponding - Cracks
- ROUGHNESS
' ' ' 
From
Structures to Processes
- From
Lattices to Structures
- Node -> Lattice
- Connection-Link -> Network
- STRUCTURE
- Ordered
- Open / Close
- Finite
- Homogeneous / Complex
- Hierarchical / Multihierarchical
- DISTIBUTIVE - DISPERSIVE
' ' '

STEP
1 : consider a number of parallel simultaneous lanches

STEP
2 : tilt the picture and let velocity depend on slope

STEP
3 : consider distribution of time arrival

DISPERSION
over a STRUCTURE
It differs from Diffusion as it may occurs only if flow is not nil

Key
Processes
Classification
- Runoff
= Surface Collection
- The flow is non-conservative (infiltration and pref.flows)
- Slope (gravity) driven
- 2 - to - 1 (Flow Collapsation)
- Over-Saturation modifies network
- Water
Transport (absorption, infiltration, redistribution, cap.rise, evaporation)
- The flow is approximatively conservative
- Capillary driven
- 1 - to - many
- Conductivity depends on Saturation
- Solute
Transport
- The flow is non conservative (transformations and adsorption)
- Dispersion of chemical and carrier are coupled (diffusion can
be neglected)
DISPERSION
process
- It differs from Signal Propagation as it affects any fourier component
- It is a candidate to represent Anomalous Diffusion
- It represent Signal Dispersion meant as differential retardation
- It can be applied both to runoff and soil water dynamics
Conclusions