It is found from a heat-flux-driven full- f gyrokinetic particle simulation that there is ion temperature gradient (ITG) turbulence across an entire L -mode-like edge density pedestal in a diverted tokamak plasma in which the ion temperature gradient is mild without a pedestal structure, hence the normalized ion temperature gradient parameter i = (d log Ti /dr) / (d log n/dr) varies strongly from high (>4 at density pedestal top/shoulder) to low (<2 in the density slope) values. Variation of density and η i is in the same scale as the turbulence correlation length, compressing the turbulence in the density slope region. The resulting ion thermal flux is on the order of experimentally inferred values. The present study strongly suggests that a localized estimate of the ITG-driven x i will not be valid due to the nonlocal dynamics of the compressed turbulence in an L -mode-type density slope. While the thermal transport and the temperature profile saturate quickly, the E×B rotation shows a longer time damping during the turbulence. In addition, a radially in-out mean potential variation is observed. © 2009 American Institute of Physics.