The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment,
reaching heliocentric distances less than $10 R_{\odot}$. Near Earth,
spacecraft measurements of fluctuating velocities and magnetic fields taken in
the time domain are translated into information about the spatial structure of
the solar wind via Taylor's "frozen turbulence" hypothesis. Near the perihelion
of SPP, however, the solar-wind speed is comparable to the Alfv\'en speed, and
Taylor's hypothesis in its usual form does not apply. In this paper, we show
that, under certain assumptions, a modified version of Taylor's hypothesis can
be recovered in the near-Sun region. We consider only the transverse,
non-compressive component of the fluctuations at length scales exceeding the
proton gyroradius, and we describe these fluctuations using an approximate
theoretical framework developed by Heinemann and Olbert. We show that
fluctuations propagating away from the Sun in the plasma frame obey a relation
analogous to Taylor's hypothesis when $V_{\rm sc,\perp} \gg z^-$ and $z^+ \gg
z^-$, where $V_{\rm sc,\perp}$ is the component of the spacecraft velocity
perpendicular to the mean magnetic field and $\bm{z}^+$ ($\bm{z}^-$) is the
Elsasser variable corresponding to transverse, non-compressive fluctuations
propagating away from (towards) the Sun in the plasma frame. Observations and
simulations suggest that, in the near-Sun solar wind, the above inequalities
are satisfied and $\bm{z}^+$ fluctuations account for most of the fluctuation
energy. The modified form of Taylor's hypothesis that we derive may thus make
it possible to characterize the spatial structure of the energetically dominant
component of the turbulence encountered by SPP.
