MATM028 Hydrodynamic Stability

Autumn Semester 2011/2012

This course examines the stability properties of inviscid and viscous flows. The course its split into four main areas:

The Kelvin-Helmholtz Instability: An inviscid instability of the interface between two parallel flows of different density. This example introduces the notion of linear instability.

Inviscid instability of parallel flows: Here we shall derive the Rayleigh stability equation, examine the stability of piecewise linear flows, examine the stability criteria for smooth flows and introduce critical layer analysis.

Viscous instability: Here we shall derive the Orr-Sommerfeld stability equation, study the linear stability of plane Poiseuille flow, look at the asymptotic theory in the inviscid limit, and examine the connection to Rayleigh's equation.

Boundary layer flows: This section looks at the uniform flow over a flat plate with arbitrary slip velocity, and discuss the stability characteristics of these boundary layers, including how the instability is initially induced into the boundary layer.

Lecture Details

Thursday 9-11 - 07AC03

Electronic Material

Lecture notes as far as we have reached:

Brief notes on multifunctions and branch cuts

Unassessed problem sheet:

Assessed problem sheet 1 (worth 12.5%):

Assessed problem sheet 2 (worth 12.5%)

MATLAB files: kh1.m, invm1.m, unbounded_shear_layer.m, two_part_plinear_blayer.m, blasius.m, invm2.m, rayleigh.m, numeric.m, pois_eigs.m, ode.m