Numerical study of turbulent-laminar patterns in MHD, rotating and stratified shear flows

Coexisting laminar and turbulent regions have been observed in several types of wall bounded flows. In Taylor Couette flow, for example, alternating helical shaped laminar and turbulent regions have been observed within a limited Reynolds number range (Prigent et al.,

2002

) and oblique laminar and turbulent bands have been seen in experiments (Prigent et al.,

2002

) and simulations (Barkley and Tuckerman,

2005

), (Duguet et al.,

2010

) of plane Couette flow for Reynolds numbers

Re

=

U

w

h

/

ν

between about 320 and 380. Here ±

U

w

is the velocity of the two walls,

h

is the half width of the wall gap and

ν

is the viscosity. In this Reynolds number range the turbulent-laminar patterns seem to sustain while at lower

Re

the flow becomes fully laminar and at higher

Re

no clear laminar patterns can be distinguished and the flow eventually becomes fully turbulent. Similar oblique laminar-turbulent bands appeared as well in direct numerical simulations (DNS) of plane channel flow for friction Reynolds numbers

Re

τ

=

u

τ

h

/

ν

=60 and 80 (Fukudome et al.,

2009

), (Tsukahara,

2010

), where

u

τ

is the friction velocity and

h

is again the gap half width.