1 Foundation of Fluid Mechanics
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that it is both real and vague, and sometimes it can only be understood and
cannot be said.
1.9 Engineering Turbulence Theory
For practical engineering turbulence theory, Prandtl is the representative
of semi-empirical theory based on phenomenology and turbulence model
theory developed later, which plays an important role in solving turbulence engineering calculation. Based on the phenomenological principle, in
1877, Joseph Valentin Boussinesq (1842–1929, as shown in Fig. 1.71) first
compared the additional shear stress (later known as the Reynolds stress)
caused by turbulent fluctuation with the viscous stress, put forward the
famous eddy viscous hypothesis, and established the analogy relationship
between the Reynolds stress and time-averaged velocity gradient. Although
the concept of eddy viscosity appeared earlier than the Reynolds equations,
it laid the foundation for later engineering turbulence. For simple near-wall
time-averaged binary flows (as shown in Figs. 1.72 and 1.73), Turbulent shear
stress (Reynolds stress) can be expressed as follows:
τ t = −ρu v = ρν t
∂u
∂ y
Fig. 1.71 Joseph Valentin Boussinesq (1842–1929, French scientist)