it's a truism that turbulence is an unsolved challenge, even if in clinical, engin­ eering or geophysical phrases. it's unusual that this continues to be principally the case even if we now know the way to unravel at once, with assistance from sufficiently huge and strong desktops, exact approximations to the equations that govern tur­ bulent flows. the matter lies no longer with our numerical approximations yet with the dimensions of the computational activity and the complexity of the recommendations we gen­ erate, which fit the complexity of actual turbulence accurately in as far as the computations mimic the true flows. the truth that we will now resolve a few turbu­ lence during this restricted experience is however a big step in the direction of the aim of complete realizing. Direct and large-eddy simulations are those numerical ideas of turbulence. They reproduce with striking constancy the statistical, structural and dynamical houses of actual turbulent and transitional flows, even though because the simula­ tions are inevitably time-dependent and 3-dimensional they call for the main complicated computing device assets at our disposal. The numerical options range from exact spectral tools and high-order finite variations to easy finite-volume algorithms derived at the precept of embedding basic conservation prop­ erties within the numerical operations. actual direct simulations unravel all of the fluid motions absolutely, and require the top useful accuracy of their numerical and temporal discretisation. Such simulations have the advantage of serious constancy whilst conducted conscientiously, and repre­ despatched a strongest software for investigating the strategies of transition to turbulence.