Selected Examples of Flow Instabilities

Abstract

Although certain fluid flow configurations perfectly satisfy all the necessary conservation laws (the conservation of mass and of momentum) and boundary conditions, they cannot be seen in nature and cannot be used as engineering designs. The reason is that these flows exist only when the boundary conditions, external forces, internal structure of the fluids and initial conditions are in accordance with the mathematical formulation perfectly. Yet, it is our common sense that none of these conditions can be perfect in nature or in engineering practice. But, on the other hand, these flow configurations can be so sensitive to the imperfection of these conditions that the flows spontaneously change their configurations and become different types of flows. Such a sharp and quick response of a fluid flow system to a small external disturbance is known as the flow instability. At the end of Chapter 6, we have seen that the lower solitary wave on a bump is unstable. Any small external disturbance, such as the small numerical noise, can result in a sharp and quick change of the solitary wave configuration.