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Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment.

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Massachusetts Institute of Technology

July 28, 2022

UK

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Last updated:

July 28, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment.

Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Course Curriculum

    • Methods of Describing Fluid Motion Unlimited
    • Kinematics of Fluid Motion – the Eulerian picture Unlimited
    • Kinematic transport theorem Unlimited
    • Forces in the Fluid Unlimited
    • Law of Momentum Conservation Unlimited
    • Relations between stress and rate-of-strain tensors Unlimited
    • Vorticity Theorem for a viscous fluid Unlimited
    • Rayleigh’s Problem – solid wall as a source of vorticity Unlimited
    • Scaling and similarity parameters Unlimited
    • A thin fluid layer flowing down an incline Unlimited
    • Lubrication approximation for flow in a thin layer Unlimited
    • A gravity current Unlimited
    • Spreading of a shallow mass on an incline Unlimited
    • Stokes flow past a sphere Unlimited
    • Oseen’s improvement for slow flow past a cylinder Unlimited
    • Aerosols and coagulation Unlimited
    • Selective withdrawal in an isothermal stratifed fluid Unlimited
    • Flow of invisid and homogeneous fluids Unlimited
    • Viscous Flow at High Reynolds Numbers Unlimited
    • Two dimensional laminar jet Unlimited
    • The effects of pressure gradient Unlimited
    • Karman’s momentum integral approach Unlimited
    • Unsteady boundary layers Unlimited
    • Oscillatory Boundary Layers Unlimited
    • Impulsive motion of a blunt body and tendency for separation Unlimited
    • Heat and energy conservation Unlimited
    • Approximations for small temperature variation Unlimited
    • Buoyancy-driven convection – The Valley Wind Unlimited
    • Buoyant plume from a steady heat source Unlimited
    • Selective withdrawl of thermally stratified fluid Unlimited
    • Dispersion of supension in a steady shear flow Unlimited
    • Dispersion in an oscillatory shear flow Unlimited
    • Rudiments of Hydrodynamic Instability Unlimited
    • Kelvin-Helmholtz Instability for continuous shear and stratification Unlimited
    • Inviscid Instability mechanism of parallel flows Unlimited
    • Viscous Effects on the Instability of parallel flows Unlimited
    • Empirical basis of Darcy’s law for seepage flow Unlimited
    • Micro-scale basis of seepage flow; Theory of homogenization Unlimited
    • Saffman-Taylor instability in porous layer – Viscous fingering Unlimited
    • Geothermal convection in porous media Unlimited
    • Geothermal Plume Unlimited
    • Rayleigh-Darcy (or Horton-Rogers-Lapwood) instability in a porous layer Unlimited
    • Thermohaline instability in a porous layer-doubly-diffusive instability Unlimited
    • Equations of Motion in Rotating Coordinates Unlimited
    • Vorticity in inviscid rotating fluids – Taylor-Proudman theorem Unlimited
    • The Shallow-Water Approximation Unlimited
    • Steady onshore wind in a shallow Sea Unlimited
    • Cyclonic current forced by a swirling wind Unlimited
    • Transient longshore wind Unlimited
    • Transient motion in a two-layered sea Unlimited
    • Coastal upwelling in a two-layered sea Unlimited

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Massachusetts Institute of Technology