  We present a method for converting a time record of turbulent velocity
measured at a point in a flow to a spatial velocity record consisting of
consecutive convection elements. The spatial record allows computation of
dynamic statistical moments such as turbulent kinetic wavenumber spectra and
spatial structure functions in a way that bypasses the need for Taylor's
Hypothesis. The spatial statistics agree with the classical counterparts, such
as the total kinetic energy spectrum, at least for spatial extents up to the
Taylor microscale. The requirements for applying the method is access to the
instantaneous velocity magnitude, in addition to the desired flow quantity, and
a high temporal resolution in comparison to the relevant time scales of the
flow. We map, without distortion and bias, notoriously difficult developing
turbulent high intensity flows using three main aspects that distinguish these
measurements from previous work in the field; 1) The measurements are conducted
using laser Doppler anemometry and are therefore not contaminated by
directional ambiguity (in contrast to, e.g., frequently employed hot-wire
anemometers); 2) The measurement data are extracted using a correctly and
transparently functioning processor and is analysed using methods derived from
first principles to provide unbiased estimates of the velocity statistics; 3)
The method is first confirmed to produce the correct statistics using computer
simulations and later applied to measurements in some of the most difficult
regions of a round turbulent jet -- the non-equilibrium developing region and
the outermost parts of the developed jet. The measurements in the developing
region reveal interesting features of an incomplete Richardson-Kolmogorov
cascade under development.
