  Mixing in fully developed incompressible turbulent flows is known to lead to
a cascade of discontinuity fronts of passive scalar fields. A one-dimensional
(1D) variant of Baker's map is developed, capturing the main mechanism
responsible for the emergence of these discontinuities. For this 1D model,
expressions for the height-distribution function of the discontinuity fronts
and structure function scaling exponents $\zeta_p$ are derived [for Kolmogorov
turbulence, $\zeta_p=\frac 23\log_3(p+1)$]. These analytic findings are in a
good agreement with both our 1D simulations, and the results of earlier
numerical and experimental studies.
