Fluid dynamics has a reputation for difficulty, and it is earned — the governing equations are nonlinear, and their most important behavior, turbulence, resists clean solutions. That is exactly why order matters. You need a firm grasp of ideal and viscous flow before turbulence stops being noise and starts being structure, and you need the analytical picture before numerical methods will mean anything.
The path climbs from applied fundamentals, through the mathematical theory, into the boundary layers and turbulence that dominate real flows, and finally to the computational tools that engineers now depend on.
Learn the fundamentals
Start with Fluid mechanics. White's text is the standard engineering introduction — continuity, momentum, Bernoulli, pipe flow, and dimensional analysis, all grounded in problems you can picture. Then deepen the theory with An introduction to fluid dynamics, Batchelor's rigorous classic, which develops the subject from the continuum and Navier-Stokes equations up. Read them together: White for intuition, Batchelor for foundations.
Master viscous and boundary-layer flow
Real fluids stick, and that changes everything near a surface. Viscous fluid flow covers exact and approximate solutions of the viscous equations, and Boundary-layer theory — Schlichting's monumental text — is the definitive treatment of the thin, high-shear region where drag and separation are decided. This stage is the hinge of the whole subject.
Confront turbulence and computation
Now the hard frontier. Turbulent Flows is the modern reference on the statistical theory of turbulence, while A First Course in Turbulence is the gentler, more physical introduction — read it first if the subject feels overwhelming. Finally, because most real problems are solved on computers, An introduction to computational fluid dynamics teaches the finite-volume methods that discretize the equations, and Computational fluid dynamics rounds out the numerical toolkit.
Follow the full path and turbulence goes from a mystery to a subject with real handles. The related differential-equations path sharpens the math these later stages demand, and the biology paths show where fluid reasoning quietly reappears in living systems.
