Course Content:
Vorticity, vorticity equation, Kelvin’s theorem, Helmholtz laws, kinematic decomposition of velocity fields, uniqueness of solenoidal and irrotational velocity fields, superposition of irrotational flows, complex analysis, conformal transformations, finite wings, threedimensional potential flows, unsteady potential flows, virtual mass, cavitation, bubble dynamics, interfacial and freesurface waves, bores and hydraulic jumps.
No. of Lectures (40 Lectures)
I. Introduction(1 lecture):
II. Vorticity dynamics (12 Lectures):

Vorticity, vortex lines and tubes, vorticity equation, circulation, Kelvin’s circulation theorem, Helmholtz laws, creation of vorticity, Helmholtz’s kinematic decomposition, BiotSavart law, inviscid motion of point vortices, line and sheet vortices, image vorticity, vortex momentum, uniqueness of solenoidal and irrotational velocity fields in singly and multiplyconnected domains, Kelvin’s minimum energy theorem, superposition of irrotational flows
III. Potential flows (17 Lectures):

Stream function and velocity potential, complex analysis, standard flow patterns, circle theorem, Blasius integral laws, conformal transformations, Jowkowski transformation, introduction to thinairfoil theory, finite wings, introduction to liftingline theory, SchwarzChristoffel theorem, axisymmetric and threedimensional potential flows, sphere theorem, nature of 3D farfields, unsteady potential flows, virtual mass
IV. Elements of bubble dynamics (3 Lectures):
V. Interfacial waves and freesurface flows (7 Lectures):

Small amplitude waves at free surfaces and interfaces, nonlinear theory of shallowwater waves, method of characteristics, bores and hydraulic jumps
Target audience:

PG and 3^{rd}, 4^{th} year UG students
Suggested Readings:

MilneThomson, L. M. “Theoretical Hydrodynamics”, 5th Ed., Dover

MilneThomson, L. M. “Theoretical Aerodynamics”, 4th Ed., Dover

Vallentine, H. R. “Applied Hydrodynamics”, 2nd Ed., Butterworths

Batchelor, G. K. “Introduction to Fluid Dynamics”, 1st Indian Ed., Foundation Books

Panton, R. L. “Incompressible Flow”, 3rd Ed., Wiley

Lighthill, J. “An Informal Introduction to Theoretical Fluid Mechanics”, Oxford Clarendon

Currie, I. G. “Fundamental Mechanics of Fluids”, 4th Ed., CRC Press
