This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent ?ows and on stochastic simulations. It is also suitable for the self-study of professionals involved in the research and modelling of large scale stochastic ?uid ?ows 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 ?uid ?ows 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 e?ects combined with the gravitational and rotational properties of large scale strati?ed ?ows over the secondary e?ects of viscosity is assumed. The latter point is corroborated by the many successful studies of ?uid v- cosity which limit its e?ects to speci?c 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].

Probability.- Statistical Mechanics.- The Monte Carlo Approach.- Spectral Methods.- Discrete Models in Fluids.- Spin-Lattice Models.- Monte Carlo Simulations of Spin-Lattice Models on the Sphere.- Polyhedra and Ground States.- Mesh Generation.- Statistical Mechanics for a Vortex Gas.- Two-Layer Quasi-Geostrophic Models.- Coupled Barotropic Vorticity Dynamics on a Rotating Sphere.

This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent ?ows and on stochastic simulations. It is also suitable for the self-study of professionals involved in the research and modelling of large scale stochastic ?uid ?ows 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 ?uid ?ows 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 e?ects combined with the gravitational and rotational properties of large scale strati?ed ?ows over the secondary e?ects of viscosity is assumed. The latter point is corroborated by the many successful studies of ?uid v- cosity which limit its e?ects to speci?c 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].