Salta ai contenuti. | Salta alla navigazione

Strumenti personali


Academic year and teacher
If you can't find the course description that you're looking for in the above list, please see the following instructions >>
Versione italiana
Academic year
Didactic period
Primo Semestre

Training objectives

The course provides the theoretical background for the study of the advection-diffusion of mass in natural and artificial free-surface streams. The course also provides the practical knowledge aimed at solving simple environmental problems related to mixing and disposal of pollutants in natural water bodies.


Basic knowledge of free surface Hydraulics. Differential and integral calculus (Fundamentals in mathematics). Basic knowledge of numerical methods and computer programming. Prerequisites: Hydraulics.

Course programme

The course includes 60 hours of teaching between lessons (45 hours) and exercises (15 hours) and will be divided as specified below:

Basic notions of the Environmental hydraulics : type of pollutants, sources and control strategies ; processes, scales and analysis tools. (2.5 hours)

The molecular diffusion: the main variables; The Fick's law; the equation of molecular diffusion for a fluid at rest and in motion; initial and boundary conditions of the equations of molecular diffusion; the 1D fundamental solution and applicability of the superposition of the effects; the 2D and 3D fundamental solutions; some analytical solutions. Influence of the walls: the method of the images. (12.5 hours)

The turbulent diffusion: fundamentals of turbulence; probabilistic tools for the study of turbulent flows; Statistical analysis of the diffusion of a cloud of pollutant; Basis of the Taylor's theory of diffusion; the equation of turbulent diffusion and the related diffusivity coefficients. (5 hours)

The hydrodynamic dispersion: a qualitative introduction of the phenomenon; the fundamental equations; The theory of Elder for channels with wide rectangular cross-sections. (5 hours)

Mixing processes in natural streams: basic concepts. Mixing in the near field: applicability of diffusive scheme; vertical mixing downstream of a transverse source. Mixing in the intermediate field: 2D equation of turbulent diffusion; estimate of the transversal turbulent diffusivity. Mixing in the far field: 1D equation of turbulent diffusion; solution for the concentration in the far field; estimate of the coefficient of longitudinal dispersion; the method of the frozen cloud. (12.5 hours)

Mixing processes of reactive solute: general aspects; modeling in a fluid at rest (dissolved oxygen concentration, sewage oxidation and BOD decay, the aeration process, the oxygen balance); modeling in a fluid in motion (BOD decay, the oxygen balance). (5 hours)

Jets and plumes: general aspects; axisymmetric jets and plumes; buoyant plumes. (2.5 hours)

Exercises in the computer lab on the topics covered in the course. (15 hours)

Didactic methods

Theoretical lessons and practical exercises.

Learning assessment procedures

The aim of the examination is to test the level of achievement of learning objectives stated above.

The student will give the teacher a brief report of the exercises done during the course. This report must be delivered to the teacher one week in advance of the exam date emailing a pdf file. This report must contain a brief summary of the theoretical basis of the exercises, a brief comment on the obtained results and the matlab scripts. The work will be evaluated on the basis of its completeness and correctness and on the presentation form.

The exam consists of an oral test on the all topics covered in the course. The test is intended to evaluate the study of themes, the understanding of the topics and the ability to connect and compare different aspects developed during the course.

During the oral exam, the exercises done during the course will be discussed in order to assess the mastery of methods and tools used by the student.

The final assessment consists of one vote, in fraction of thirty, corresponding to an overall judgment on the exam. As an indication, the final judgment will depend for a 15% from the report evaluation; for a 15% from the evaluation of the exercises discussion and for the remainder of the outcome of the oral examination on the topics covered in the course.

Reference texts

Lanzoni S., “Fenomeni di mescolamento nei corsi d'acqua”, Lecture Notes, Faculty of Engineering, Padova University;

Seminara G. & Tubino M., “Appunti di Idraulica Ambientale, Fondamenti sulla diffusione e dispersione di traccianti passivi”, Lecture Notes, Faculty of Engineering, Genoa University;

Seminara G. & Tubino M., “Appunti di Idraulica Ambientale, Facoltà di Ingegneria”, Lecture Notes, Genoa University, 2005;

Socolofsky S.A. & Jirka G.H., “Special Topics in Mixing and Transport Processes in the Environment”, Lecture Notes, “Coastal and Ocean Engineering Division Texas A&M University”, 2005;

Fischer, J.L., Imberger, List, Koh and Brooks, “Mixing in Inland and Coastal waters”, Academic Press, 1976;

Rutherford J.C., “River Mixing”, Jhon Wiley & Sons, Chichester, 1994.

Lee J.H. and Chu V.H., “Turbulent jets and plumes – a lagrangian approach”, Springer, 2003.