Module Code - Title:
MA6002
-
MATHEMATICAL GEOSCIENCE
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
Prerequisite Modules:
Rationale and Purpose of the Module:
Syllabus:
Climate dynamics.
Radiative heat transfer. Greenhouse effect.
Enhanced greenhouse effect. Convection.
Energy balance models. Weathering, the carbon cycle.
Ice ages.
Rivers
Chezy and Manning flow laws.
Slowly varying flow; flood hydrograph.
Rapidly varying flow, St. Venant equations.
Steady states; waves, shocks; instability, roll waves.
Tidal bores.
Sediment transport
Patterns and bedforms.
Bedload transport; the Exner equation. Suspended sediment. Potential flow model.
St. Venant type models.
Anti-dunes and dunes. Bars, meanders, deltas.
Convection
Mantle convection. Rayleigh-Benard convection:
linear stability, boundary layer convection.
Double diffusive convection.
Convection in a slot: volcanic vents, fingering. Plumes.
Glacier dynamics
Glacier flow, ice sheets. The shallow ice approximation.
Ice shelves, the grounding line. Waves and surges.
Surface waves. Subglacial sliding.
Subglacial drainage. Seasonal waves.
Linked cavity systems and surges.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
1. Develop the ability to build mathematical models for environmental systems involving o.d.e.s and p.d.e.s
Final exam and homework for credit.
2. Learn physical principles necessary to model-building, including radiative heat transfer, sediment transport, ice dynamics.
Final exam and homework for credit.
3. Understand principles of wave and stability theory.
Final exam and homework for credit.
4. Use and application of boundary layer theory in applications.
Final exam and homework for credit.
5. Understand model applications in climate dynamics, river flow, convection and glacier flow. Final exam and homework for credit.
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Paterson, W. S. B (1999)
The physics of glaciers (3e)
, Butterworth-Heinemann
Houghton, J. T. (2002)
The physics of atmospheres (3e)
, Cambridge University Press.
Other Relevant Texts:
Turner, J.S. (1979)
Buoyancy effects in fluids
, Cambridge University Press
Batchelor, G.K., Moffatt, H.K. and Worster, M.G. (eds.) (2000)
Perspectives in fluid dynamics
, Cambridge University Press.
Richards, K (1982)
Rivers
, Methuen
Whitham, G.B. (1974)
Linear and nonlinear waves
, Wiley
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
Andrew.Fowler@ul.ie