  In this survey, we review the results on turbulence for the generalised
Burgers equation on the circle: u_t+f'(u)u_x=\nu u_{xx}+\eta,\ x \in S^1=\R/\Z,
obtained by A.Biryuk and the author in \cite{Bir01,BorK,BorW,BorD}. Here, f is
smooth and strongly convex, whereas the constant 0<\nu << 1 corresponds to a
viscosity coefficient. We will consider both the case \eta=0 and the case when
\eta is a random force which is smooth in x and irregular (kick or white noise)
in t. In both cases, sharp bounds for Sobolev norms of u averaged in time and
in ensemble of the type C \nu^{-\delta}, \delta>=0, with the same value of
\delta for upper and lower bounds, are obtained. These results yield sharp
bounds for small-scale quantities characterising turbulence, confirming the
physical predictions \cite{BK07}.
