Interdisciplinarity for Natural Sciences


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

' ' '

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

DISPERSION process

Conclusions