A geometric wedge model of the near-earth nightside plasma sheet is used to
derive a wave equation for low frequency shear flow-interchange waves which
transmit E×B sheared zonal flows along magnetic flux tubes
towards the ionosphere. Discrepancies with the wave equation result used in
Kalmoni et al. (2015) for shear flow-ballooning instability are discussed. The
shear flow-interchange instability appears to be responsible for substorm
onset. The wedge wave equation is used to compute rough expressions for
dispersion relations and local growth rates in the midnight region of the
nightside magnetotail where the instability develops, forming the auroral beads
characteristic of geomagnetic substorm onset. Stability analysis for the shear
flow-interchange modes demonstrates that nonlinear analysis is necessary for
quantitatively accurate results and determines the spatial scale on which the
instability varies