  Sweet-Parker current sheets in high Lundquist number plasmas are unstable to
tearing, suggesting they will not form in physical systems. Understanding
magnetic reconnection thus requires study of the stability of a current sheet
as it forms. Formation can occur due to sheared, sub-Alfv\'enic incompressible
flows which narrow the sheet. Standard tearing theory (Furth et al. 1963; Coppi
et al. 1976; Rutherford 1973) is not immediately applicable to such forming
sheets for two reasons: first, because the flow introduces terms not present in
the standard calculation; second, because the changing equilibrium introduces
time dependence to terms which are constant in the standard calculation,
complicating the formulation of an eigenvalue problem. This paper adapts
standard tearing mode analysis to confront these challenges. In an initial
phase when any perturbations are primarily governed by ideal MHD, a coordinate
transformation reveals that the flow compresses and stretches perturbations. A
multiple scale formulation describes how linear tearing mode theory (Furth et
al. 1963; Coppi et al. 1976) can be applied to an equilibrium changing under
flow, showing that the flow affects the separable exponential growth only
implicitly, by making the standard scalings time-dependent. In the nonlinear
Rutherford stage, the coordinate transformation shows that standard theory can
be adapted by adding to the stationary rates time dependence and an additional
term due to the strengthening equilibrium magnetic field. Overall, this
understanding supports the use of flow-free scalings with slight modifications
to study tearing in a forming sheet.
