# PHY3041 : Advanced Fluid Dynamics

• Offered for Year: 2019/20
• Module Leader(s): Professor Carlo Barenghi
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5

#### Aims

To present advanced topics of fluid dynamics building on the introductory concepts developed in PHY2033.

Module Summary
To introduce the mathematical tools to model two-dimensional inviscid flows more advanced than seen in PHY2033 and to predict the motion of realistic viscous flows using the Navier-Stokes equation. To illustrate the variety of solutions of the Navier-Stokes equation in the physical world, paying attention to topics such as transitions of flow patterns, and including applications to flying, weather and climate.

#### Outline Of Syllabus

Review of elementary fluid dynamics presented in MAS2803 (e.g. continuity equation, Euler equation, vorticity, stream function, complex potential for two-dimensional flows). More advanced
complex complex potential methods to include singularities (sources, vortices), boundaries (method of images, Milne-Thomson theorem), Magnus force (lift) and Hamiltonians. Microscopic and macroscopic description of viscosity. The Navier-Stokes equation. No-slip boundary conditions. Analytic solutions of the Navier-Stokes equation (e.g. channel flows in Cartesian and cylindrical geometries, Couette flows, oscillating flows). Transitions to complex vortex flows (flows past
cylinder, Taylor-Couette, Rayleigh-Benard and Reynolds problems). Dimensionless variables, Reynolds number, introduction to turbulence, drag. Flows in rotating frames: Coriolis, centrifugal and Poincare forces. Simple applications to weather and climate.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen Exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen Exam
Guided Independent StudyAssessment preparation and completion26:0012:00Preparation for coursework assignments
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study33:009:00Revision for coursework assignments and class test
Guided Independent StudyIndependent study125:0025:00Studying, practising and gaining understanding of course material
Total100:00
Code Title
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A90N/A
Written Examination401M5Class test
##### Exam Pairings
Module Code Module Title Semester Comment