What you will learn
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Fluid systems
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capillary-gravity
The course is an introduction to the rich field of interfacial waves. The first half of the course prepares the student for studying wave phenomena by introducing discrete mechanical analogues of wave phenomena in fluid systems. The basic principles of normal mode analysis are introduced through point-mass systems connected through springs. The exact solution to the (nonlinear) pendulum equation is used to introduce the notion of amplitude dependence on frequency of the oscillator. The Kapitza pendulum is introduced as a discrete analogue for Faraday waves. Basic perturbation techniques are then introduced for subsequent use. The second half of the course introduces basics of interfacial waves viz. shallow and deep-water approximations, phase and group velocity, frequency and amplitude dispersion etc.. Capillary as well as capillary-gravity waves in various base state geometries (rectilinear, spherical (drops and bubbles including volumetric oscillations of the latter), cylindrical (filaments) are taught and the corresponding dispersion relation derived. The Stokes travelling wave is derived using the Lindstedt-Poincare technique and the amplitude dependence in the dispersion relation is highlighted. Side-band instability of the Stokes wave is discussed. Fluid particle trajectories for linear water waves is derived and the Stokes drift expression is derived. Time permitting, the Kelvin ship wave pattern in deep water is derived using the method of stationary phase. Introductory ideas in resonant interactions among surface gravity waves are discussed. The fundamental aspects studied in the course will be related to various engineering applications continuously.
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Meet Your Instructor
About Instructor
VTU is one of the largest Technological Universities in India with 24 years of Tradition of excellence in Engineering & Technical Education, Research and Innovations. It came into existence in the year 1998 to cater the needs of Indian industries for trained technical manpower with practical experience and sound theoretical knowledge.
Free
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Course Duration30 h 25 m 18 s
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Course LevelIntermediate
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Student Enrolled0
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LanguageEnglish
This Course Includes
- 30 h 25 m 18 s Video Lectures
- 0 Quizzes
- 0 Assignments
- 0 Downloadable Resources
- Full Lifetime Access
- Certificate of Completion