### 2021　Fluid Mechanics (EPS course)

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Undergraduate major in Earth and Planetary Sciences
Instructor(s)
Okamoto Taro
Course component(s)
Lecture    (その他)
Day/Period(Room No.)
Group
-
Course number
EPS.B330
Credits
2
2021
Offered quarter
1Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

Fluid mechanics has profound importance in Earth and planetary sciences because various phenomena on the Earth and planets are related to the dynamic motion of the fluids. This course is designed as an introductory course for fluid mechanics for Earth and planetary sciences: it begins with fundamental aspects of fluid mechanics and will deal with typical fluid motions in the field of Earth and planetary sciences.

### Student learning outcomes

By completing this course, students will able to
(1) Understand the basic terms and equations of the fluid mechanics,
(2) Understand the basic aspects of the flow of inviscid, incompressible fluid,
(3) Understand the basic aspects of the flow of viscous fluid,
(4) Understand the basic aspects of the fluid mechanical stability.

### Keywords

inviscid and incompressible fluids, viscous fluids, geophysical fluid dynamics

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills ✔ Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

This course mainly consists of lectures. Discussions will be held about exercises.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Ideal fluids (1): motion of fluids Understand how to describe the motion of the fluids.
Class 2 Ideal fluids (2): the equation of continuity and the Euler equation Understand the equation of continuity and the Euler equation.
Class 3 Ideal fluids (3): the Bernoulli's theorem Understand the Bernoulli's theorem.
Class 4 Ideal fluids (4): the Kelvin's circulation theorem Understand the Kelvin's circulation theorem.
Class 5 Ideal fluids (5): incompressible, irrotational flow Understand the potential description of incompressible irrotational flow.
Class 6 Ideal fluids (6): two-dimensional incompressible irrotational flow Understand the potential description of incompressible irrotational flow in two dimensions. Describe the Blasius theorem and the Kutta-Zhukovsky theorem.
Class 7 Ideal fluids (7): gravity waves Understand the gravity waves which are the wave motions with the restoring force due to the gravity.
Class 8 Viscous fluids (1): the stress tensor Understand the stress tensor in the viscous flow.
Class 9 Viscous fluids (2): representation of the stress tensor Understand the stress tensor and constitutive relations.
Class 10 Viscous fluids (3): the Navier-Stokes equation Understand the Navier-Stokes equation
Class 11 Viscous fluids (4): typical visous flows, the similarities in viscous flows, the Raynolds number Understand some typical visous flows, the similarities in viscous flows, and the Raynolds number.
Class 12 Viscous fluids (5): Viscous flows at small Raynolds number Understand viscous flows at small Raynolds number
Class 13 Viscous fluids (6): the concept of stability and its application to thermal convection  Understand how to describe the concept of stability mathematically and its application to thermal convection
Class 14 Viscous fluids (7): the concept of stability and its application to thermal convection  Understand how to describe the concept of stability mathematically and its application to thermal convection

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class. They should do so by referring to textbooks and other course material.

None

### Reference books, course materials, etc.

Fluid Mechanics, Landau & Lifshitz, Butterworth-Heinemann

### Assessment criteria and methods

Student's knowledge and understanding of fluid mechanics are assessed by contents of reports.

### Related courses

• EPS.B203 ： Mechanics (EPS course)
• EPS.B212 ： Electromagnetism (EPS course)
• EPS.B201 ： Mathematics for Physics A (EPS course)
• EPS.B210 ： Mathematics for Physics B (EPS course)
• EPS.B202 ： Thermodynamics (EPS course)

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is recommended to complete the courses of Mechanics (EPS course), Electromagnetism (EPS course), Mathematics for Physics A (EPS course), Mathematics for Physics B (EPS course) and Thermodynamics (EPS course) before taking this course. 