Remote generation of electromagnetic waves in the terahertz (THz) by the volume of air medium gains increasing scientific interest due to the demand for this spectral range in solving various practical problems including those belonging to the nonlinear atmospheric optics. During self-focusing and filamentation of high-power femtosecond laser pulses in air, the source of THz radiation is the plasma of laser filaments. One of the main challenges of THz generation by a laser filament is increasing the value of optical energy conversion to the long-wavelength band. In this paper, we present the results of our studies on DC-biased THz generation during single-color filamentation in air of focused femtosecond Ti:Sapphire-laser pulses (800 nm, pulse energy up to 40 mJ). The distinctive feature of our study is that a femtosecond optical pulse propagates through a spatially-localized heated air layer containing randomly inhomogeneous refractive index perturbations, which mimics strong air turbulence. For the first time to our knowledge, we show, that the turbulent air layer formed at the beginning of the optical path allows increasing the yield of THz radiation up to 1.5 times due to the formation of multiple chaotically-arranged filaments resulting from random perturbations of the optical beam energy profile that reduces the subsequent THz (re)absorption in the filament plasma.