In the tokamak Tore Supra, when a poloidally and toroidally localized limiter, called a modular limiter, is introduced into the lower part of the scrape-off layer, density fluctuations located in the vicinity of this limiter present a specific feature with the appearance of a new spectral pattern in the associated frequency spectrum. This leads to a strong up-down asymmetry observed in both the plasma edge and the plasma outer core, with a maximum level of turbulence at the bottom of the plasma. The observed asymmetry characteristics show that magnetic connection lengths play a critical role here and that the limiter configuration has some effect on the outer core turbulence.