Langevin Stochastic Equations: Treatment of Ocean, Planetary Boundary Layer, and Stellar Turbulence

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.

Vittorio M. Canuto, born in Torino, Italy, completed classical studies at a Salesian school and earned a doctorate in theoretical physics from the University of Torino. Since 1968, he has been a NASA staff scientist at the Goddard Institute for Space Studies in New York, with a sabbatical year at Nordita in Copenhagen. He is currently an adjunct professor at Columbia University. In 1980, he was appointed Scientific Advisor to the Holy See at the United Nations, where he helped bring attention to space debris in 1988. He has organized symposia for the Pontifical Academy of Sciences and authored three books, including Il Paradosso Nucleare. Pope John Paul II awarded him the Order of St. Gregory the Great in 1985. Dr. Canuto’s research spans low-temperature and nuclear physics, neutron stars, pulsars, and cosmology, including collaboration with Nobel laureate P.A.M. Dirac. Since 1985, he has focused on turbulence in stars, oceans, and planetary boundary layers. He has also advised the Italian Ministry of the Environment and is part of a scientific advisory group for ENEA, Italy’s research agency. On climate change, he has written for Encyclopedia Treccani, explaining the topic for general readers. His hobbies include opera and supporting Juventus.