Hello, I would be grateful if anyone can explain me following things: 1. free shear flow 2. stress driven secondary flows 3. viscous damping 4. kinematic blocking 5. viscous heating.

Many Thanks, Regards,

1. not sure. I know what's a shear flow, not sure what the "free" term means. A shear flow is when two layers of fluid parallel to each other and moving parallel to each other have different velocities, namely there is a velocity gradient across the direction perpandicular to the flow velocity. Shear-free would mean there is no shear, but free shear... I've got no clue what it is meant by that.

2. Usually one talks about secondary flows emerging from instabilities, my guess would be that here the secondary flows are emerging from the stress. Usually the secondary flows take the form of some convection movements, such as convective cells in a heated from below flow (Rayleigh Taylor instability) or Goertler vortices forming due to a centrifugal instability. The stress can be perpandicular or tangential, and the tangential component (called shear) can easily create the shearing (Kevlin-Helmoholtz) instability which creates vortices locally (a kind of secondary flow - though usually it diverge into turbulence).

3. viscous damping. Here the flow is "slowed down" by the viscousity. If there is a sharp edge wave, its amplitude is decreased and its profile is smoothed out due to the "diffusive" effect of the viscosity. E.g. oscillations or sound waves can be "damped" by viscous effects, that means that their amplitude will decrease with time (viscosity is like internal friction). The viscosity enters the equations with a second derivative in time, that's a diffusive term, and therefore there is dissipation due to that term. This (kinetic) energy that is dissipated is not lost, as energy is conserved, and this dissipated kinetic energy is transformed into heat (see 5.)

4. no idea.

5. As the sharp and find structure of a flow can be "damped" by the viscosity, the flow is actually losing energy due to the internal friction (=viscosity) and as a result the flow heats up. So the energy of the flow (say kinetic energy \rho v^2 ) is usually dissipated due to the viscous friction/dissipation and as a result of that this kinetic energy is transformed into thermal energy (heat) to increase (locally) the temerature of the flow. For this you need to look into the energy flux equation of the flow.

ad 1.) Free shear flow means a shear flow in the absence of walls (in contrast to boundary layers). The most prominent example is the free shear layer.

Sorry, on (3), it is a second derivative in space, not a second derivative in time, sorry for the typo and for other misspelling mistakes...

also 5. is equivalent to the second laws of thermodynamics, namely that there is always some work "lost" to heating the system due to friction, etc...; actually the energy equation itself is based on the 1st and 2nd laws of thermodyanmics.

Very well explained. Thank you very much Patrick!