The symbol on the left side of (3.13) should be the same as defined in (2.12), namely,
$\unicode[STIX]{x1D6E9}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D702})$
.
The two
$qN-M$
factors in (2.21) should be replaced with
$N-q^{-1}M$
. Then, above (2.27) the statement should read ‘the radial variation of
$N-q^{-1}M$
is negligible if
$1-qN/M\gg Rq^{-1}\unicode[STIX]{x2202}q/\unicode[STIX]{x2202}r$
’.
In addition, for the superbanana plateau regime (sbp) the evaluation of (3.13) needs to be slightly different than the
$\sqrt{\unicode[STIX]{x1D708}}$
regime procedure presented in (3.14) to (3.16). For the sbp regime the boundary layer is at
$\unicode[STIX]{x1D705}_{0}^{2}\simeq 0.83$
, rather than the trapped–passing boundary. Therefore,
$\unicode[STIX]{x1D702}_{t}$
should be replaced by
$\unicode[STIX]{x1D702}_{0}\equiv 2\sin ^{-1}\unicode[STIX]{x1D705}_{0}\simeq 2.3$
in (3.13), (3.14) and (3.15) for the sbp case. As a result, the
$\cos [(qn-m)\unicode[STIX]{x03C0}/(qN-M)]$
term in (3.16), (3.18), (7.8), (7.13), (7.14), (7.16) and (7.17) should be replaced by
$\cos [(qn-m)\unicode[STIX]{x1D702}_{0}/(qN-M)]$
. For the same reason,
$\cos (qn\unicode[STIX]{x03C0})$
must be replaced by
$\cos (qn\unicode[STIX]{x1D702}_{0})$
in (7.18) and (7.19).
Acknowledgements
Work supported by the US Department of Energy grant DE-FG02-91ER-54109.
