  In this paper we introduce a new PDE model in frequency space for the
inertial energy cascade that reproduces the classical scaling laws of
Kolmogorov's theory of turbulence. Our point of view is based upon studying the
energy flux through a continuous range of scales rather than the discrete set
of dyadic scales. The resulting model is a variant of Burgers equation on the
half line with a boundary condition which represents a constant energy input at
integral scales. The viscous dissipation is modeled via a damping term. We show
existence of a unique stationary solution, both in the viscous and inviscid
cases, which replicates the classical dissipation anomaly in the limit of
vanishing viscosity.
  A survey of recent developments in the deterministic approach to the laws of
turbulence, and in particular, to Onsager's conjecture is given.
