This thesis investigates three major topics for a spatially developing turbulence using direct numerical simulations. The subjects of this study are: (i) velocity gradients in fluid turbulence, (ii) temperature gradients in scalar turbulence and (iii) heat transfer from a cylinder due to free-stream turbulence. A square grid-element is used to generate fluid, scalar and free-stream turbulence. The square grid-element is a fundamental building block to both the classical and fractal grids. The large-scale terms of fluid and scalar turbulence are generated mainly behind the bars of the grid-element due to the action of mean velocity and scalar gradients. On the other hand, the small-scale terms are generated behind the bar predominately by the stretching/compressing of fluctuating velocity and scalar gradient vectors by the turbulent strain-rate. These quantities are then transported to the grid-element centreline through the action of turbulent transport. The best defined -5/3 slope of the turbulent velocity and scalar spectra is observed close to the grid-element where the turbulence is highly inhomogeneous and the small-scale terms have just started developing. The universal characteristics of velocity and scalar gradients are observed in the far-downstream where the turbulence is approximately homogeneous and the values of Taylor-length-based Reynolds and Corrsin-length-based Peclet numbers are very low. The inhomogeneous production region of the grid-element is observed to increase heat transfer from a cylinder substantially although its turbulent intensity is similar to that of the homogeneous decay region. It is noted that the turbulence in the production region is unique with its dominant frequency of fluctuations close to the shedding frequency and with the prevalence of azimuthal vortical structures which start increasing the heat transfer even before they get stretched by the accelerating boundary layer.