This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent flows and on shastic simulations. It is also suitable for the self-study of professionals involved in the research and modelling of large scale shastic—fluid flows with a substantial vortical component. Several related ideas motivate the approach in this book, namely, the application of equilibrium statistical mechanics to two-dimensional and 2- dimensional fluid flows in the spirit of Onsager [337], and Kraichnan [227], is taken to be a valid starting point, and the primary importance of non-linear convection effects combined with the gravitational and rotational properties of large scale stratified flows over the secondary effects of viscosity is assumed. The latter point is corroborated by the many successful studies of fluid v- cosity which limit its effects to specific and narrow regions such as boundary layers, and to the initial and transient phases of the experiment such as in the Ekman layer and spin-up [154] [344].