  The paper addresses two unusual scaling regimes (types of critical behaviour)
predicted by the field-theoretic renormalization group analysis for a
self-organized critical system with turbulent motion of the environment. The
system is modelled by the anisotropic stochastic equation for a "running
sandpile" introduced by Hwa and Kardar in [{\it Phys. Rev. Lett.} {\bf 62}:
1813 (1989)]. The turbulent motion is described by the isotropic
Kazantsev-Kraichnan "rapid-change" velocity ensemble for an incompressible
fluid. The original Hwa-Kardar equation allows for independent scaling of the
spatial coordinates $x_{\parallel}$ (the coordinate along the preferred
dimension) and ${\bf x_{\bot}}$ (the coordinates in the orthogonal subspace to
the preferred direction) that becomes impossible once the isotropic velocity
ensemble is coupled to the equation. However, it is found that one of the
regimes of the system's critical behaviour (the one where the isotropic
turbulent motion is irrelevant) recovers the anisotropic scaling through
"dimensional transmutation." The latter manifests as a dimensionless ratio
acquiring nontrivial canonical dimension. The critical regime where both the
velocity ensemble and the nonlinearity of the Hwa-Kardar equation are relevant
simultaneously is also characterized by "atypical" scaling. While the ordinary
scaling with fixed infra-red irrelevant parameters is impossible in this
regime, the "restricted" scaling where the times, the coordinates, and the
dimensionless ratio are scaled becomes possible. This result brings to mind
scaling hypotheses modifications (Stell's weak scaling or Fisher's generalized
scaling) for systems with significantly different characteristic scales.
