He then moved to the United Kingdom where he completed his doctorate in geophysical fluid dynamics from Cambridge University in 1969, on rotating and stratified flows, and double-diffusive convection.

[4] Baines moved back to Australia as a Queen's Fellow in Marine Science in 1971, and joined CSIRO Division of Atmospheric Physics in 1973 as a senior research scientist.

His doctoral thesis included work on forced wave motion in rotating and stratified fluids, and a fundamental study of the nature of double-diffusive convection.

This led to a significant number of papers describing theoretical, numerical and experimental studies of the flow of density-stratified fluids over and around topography with a variety of two- and three-dimensional shapes.

In a review by Xin-she Yang from University of Leeds, the book is declared having "good balance of basic principles, theory, and experiment, where the comparison is made whenever possible, with a consistent attempt to provide a physical understanding of the phenomena involved."

[15] Don L. Boyer of Arizona State University considers the book as "an invaluable reference for students and research workers" and congratulated Baines for "very fine piece of work".

Boyer also states that "one fact that cannot escape the reader is that the author, Dr. Baines combines the mastery of the analysis involved with an outstanding facility in laboratory experiment", which he considers "very rare indeed in the scientific community".

[19] Baines worked on climate dynamics from 2005 till 2014 and published various research articles on topics that included the zonal structure of the Hadley circulation, and the effect of the African monsoon on the rainfall of southwest Western Australia.

His research concluded that seasonal rainfall in Australia is dependent on several dynamic processes but mostly on El Niño-Southern Oscillation and the Indian Ocean Dipole.

In 2013 Baines, along with Selwyn Sacks, wrote an article entitled 'Atmospheric internal waves generated by explosive volcanic eruptions' for the UK Geological Society Memoirs volume on the Soufriere Hills volcano on Montserrat.