1 Foundation of Fluid Mechanics
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In the nineteenth century, fluid mechanics focused on solving the problems and solutions of the theory of irrotational motion of the ideal fluid and
established the theory of vortex motion of ideal fluid and the equation of
viscous fluid mechanics. With the application of ideal fluid mechanics as the
core, the ideal incompressible irrotational flow around different objects was
solved. For example, the potential flow solutions around spheres, cylinders,
and angular flows are obtained. Based on the potential flow superposition
principle, the potential flow singularity solution was proposed. In 1813,
French mathematician Augustin Louis Cauchy (1789–1857, as shown in
Fig. 1.19) proposed the complex variable function. In 1850, the German
mathematician Georg Friedrich Bernhard Riemann (1826–1866, as shown
in Fig. 1.20) completed the single-valued condition for the complex variable
function to be an analytic function. In 1868, Hermann Ludwig Ferdinand
von Helmholtz (1821–1894, as shown in Fig. 1.21), the German hydromechanist, established a potential flow method of complex variable function based
on flow function and potential function (as shown in Fig. 1.22). At the
same time, Helmholtz put forward the velocity decomposition theorem of
fluid mass in 1858, studied the swirling motion of ideal incompressible
fluid under the action of force, and put forward three laws of Helmholtz’s
swirling motion, namely, the law of invariance of vorticity intensity along the
vortex tube, the law of keeping vorticity tube, and the law of conservation
of vorticity intensity. And the theory of vortex motion of the ideal fluid was
established. In 1882, the British scientist W. J. M. Rankine (1820–1872, as
Fig. 1.19 Augustin Louis Cauchy (1789~1857, French mathematician and fluid
mechanist)
19
In the nineteenth century, fluid mechanics focused on solving the problems and solutions of the theory of irrotational motion of the ideal fluid and
established the theory of vortex motion of ideal fluid and the equation of
viscous fluid mechanics. With the application of ideal fluid mechanics as the
core, the ideal incompressible irrotational flow around different objects was
solved. For example, the potential flow solutions around spheres, cylinders,
and angular flows are obtained. Based on the potential flow superposition
principle, the potential flow singularity solution was proposed. In 1813,
French mathematician Augustin Louis Cauchy (1789–1857, as shown in
Fig. 1.19) proposed the complex variable function. In 1850, the German
mathematician Georg Friedrich Bernhard Riemann (1826–1866, as shown
in Fig. 1.20) completed the single-valued condition for the complex variable
function to be an analytic function. In 1868, Hermann Ludwig Ferdinand
von Helmholtz (1821–1894, as shown in Fig. 1.21), the German hydromechanist, established a potential flow method of complex variable function based
on flow function and potential function (as shown in Fig. 1.22). At the
same time, Helmholtz put forward the velocity decomposition theorem of
fluid mass in 1858, studied the swirling motion of ideal incompressible
fluid under the action of force, and put forward three laws of Helmholtz’s
swirling motion, namely, the law of invariance of vorticity intensity along the
vortex tube, the law of keeping vorticity tube, and the law of conservation
of vorticity intensity. And the theory of vortex motion of the ideal fluid was
established. In 1882, the British scientist W. J. M. Rankine (1820–1872, as
Fig. 1.19 Augustin Louis Cauchy (1789~1857, French mathematician and fluid
mechanist)