Langevin Stochastic Equations

This book derives, solves, and assesses the Langevin Stochastic Equations (LSE) as a tool for treating turbulent flows. Previous work has demonstrated the LSE's ability to successfully describe non-geophysical turbulent flows. However, this book specifically focuses on geophysical flows. Chapter I addresses the modeling of oceanic mesoscales (M) and sub-mesoscales (SM), while Chapter II discusses vertical mixing.

The target audience for this book is advanced students and researchers interested in future climate change and the crucial role played by the ocean. One of the main challenges in describing oceanic M and SM is that they are governed by non-linear interactions for which no satisfactory model exists. Despite the unsuccessful attempts to describe non-linearity using the traditional Navier-Stokes Equations (NSE), heuristic models continue to be used. This has created a dilemma: while future climate projections need to be predictive, the heuristic treatment of M and SM lacks predictive power, leading to an internal inconsistency.

The primary goal of this book is to demonstrate that the transition from NSE to LSE resolves this inconsistency, paving the way for a fully predictive treatment of M and SM. This advancement is crucial for providing future climate predictions with the credibility they require.