1 Foundation of Fluid Mechanics
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boundary layer was studied. In 1938, the British scientist Howard studied the
problem of flow around the right angle and so on.
During this period, various viscous laminar boundary layer problems were
approximated with the help of similarity assumption. For example, in 1929,
the German scholar Tollmien obtained the Gaussian solution of the laminar
wake of a flat plat;, in 1933, the German scholar Schlichting solved the
similar solution of a circular laminar jet; and in 1945, the German scholar
Mangler introduced a similar transformation to transform the axisymmetric
laminar boundary layer problem into a plane boundary layer problem, and
solved the flow around a cone.
The viscous flow and the similarity condition of a thin layer on the wall
are the important basis for establishing the boundary layer theory of objects
with high Reynolds number.
1.6 Laminar Flow Transition Phenomenon
and Stability Theory
However, there are many flows in nature, which are not laminar flow, but
turbulent flow, which is more complex and more urgent for practical application. Therefore, the study of turbulence has begun to attract great attention.
There are two branches of research, one is the transition problem of layer
loss stability and the other is the fully developed turbulence problem. For the
first transition problem, as early as 1839, Hagen, the German scholar, found
that the flow characteristics in a circular pipe are related to the velocity. In
1869, two different flow regimes were found to have different flow characteristics. In 1880, the British scholar Osborne Reynolds (1842–1912, as shown
in Fig. 1.43) carried out a well-known transition experiment in a circular
tube (as shown in Figs. 1.44 and 1.45). In 1883, the concept of laminar flow
and turbulence was proposed, and a dimensionless number (hereinafter called
Reynolds number) was used as a criterion to give the Reynolds number 2000
(now 2320). In 1872, William Froude (1810–1879, as shown in Fig. 1.46),
the British scholar, observed that the resistance of a flat plate was proportional
to the power of 1.85 of the velocity, rather than the power of the laminar flow.
In 1914, Prandtl put forward the concept of a turbulent boundary layer when
he studied the spherical drag. In 1924, the Dutch scholar Burgers studied the
transition of boundary layer. In 1934, the American scholar Dryden gave the
critical Reynolds number (calculated by the thickness of boundary layer) for
the transition of the flat plate boundary layer, which was 2740. In 1946, he
raised this number to 8700.
39
boundary layer was studied. In 1938, the British scientist Howard studied the
problem of flow around the right angle and so on.
During this period, various viscous laminar boundary layer problems were
approximated with the help of similarity assumption. For example, in 1929,
the German scholar Tollmien obtained the Gaussian solution of the laminar
wake of a flat plat;, in 1933, the German scholar Schlichting solved the
similar solution of a circular laminar jet; and in 1945, the German scholar
Mangler introduced a similar transformation to transform the axisymmetric
laminar boundary layer problem into a plane boundary layer problem, and
solved the flow around a cone.
The viscous flow and the similarity condition of a thin layer on the wall
are the important basis for establishing the boundary layer theory of objects
with high Reynolds number.
1.6 Laminar Flow Transition Phenomenon
and Stability Theory
However, there are many flows in nature, which are not laminar flow, but
turbulent flow, which is more complex and more urgent for practical application. Therefore, the study of turbulence has begun to attract great attention.
There are two branches of research, one is the transition problem of layer
loss stability and the other is the fully developed turbulence problem. For the
first transition problem, as early as 1839, Hagen, the German scholar, found
that the flow characteristics in a circular pipe are related to the velocity. In
1869, two different flow regimes were found to have different flow characteristics. In 1880, the British scholar Osborne Reynolds (1842–1912, as shown
in Fig. 1.43) carried out a well-known transition experiment in a circular
tube (as shown in Figs. 1.44 and 1.45). In 1883, the concept of laminar flow
and turbulence was proposed, and a dimensionless number (hereinafter called
Reynolds number) was used as a criterion to give the Reynolds number 2000
(now 2320). In 1872, William Froude (1810–1879, as shown in Fig. 1.46),
the British scholar, observed that the resistance of a flat plate was proportional
to the power of 1.85 of the velocity, rather than the power of the laminar flow.
In 1914, Prandtl put forward the concept of a turbulent boundary layer when
he studied the spherical drag. In 1924, the Dutch scholar Burgers studied the
transition of boundary layer. In 1934, the American scholar Dryden gave the
critical Reynolds number (calculated by the thickness of boundary layer) for
the transition of the flat plate boundary layer, which was 2740. In 1946, he
raised this number to 8700.