Laminar flow and turbulent flow are a characteristic of fluid flow.

When a fluid flows, if the trajectory of a fluid particle (generally speaking, it changes with the initial spatial coordinates x, y and z with time t) is a regular smooth curve (in the simplest case, it is a straight line), this flow is called laminar flow, and the flow without this property is called turbulent flow. In 1959, J. Hinze once defined turbulence as the irregular movement of fluid, and various quantities in the flow field change in disorder with time and space coordinates, but statistically speaking, their accurate average values can be obtained.

In a straight pipe with a diameter of d, if the average velocity of the fluid is v, theRe is a critical value (about 2300 ~ 2800) recr for the Reynolds number of the fluid kinematic viscosity v, if re

Reynolds made experiments with glass tubes in 1883 to distinguish between laminar and turbulent conditions. Dyeing the experimental fluid, we can see that the colored particles are all laminar and straight. When Reynolds number exceeds the critical value Recr, we can see that particles are randomly mixed, and when there are pulsations in time and space, it is turbulence.

It is difficult to describe this flow by statistics and probability theory without introducing the average value of a certain quantity. Besides the turbulence in straight pipes, there are many kinds of turbulence with different characteristics. Although a lot of experiments and theoretical studies have been done, a unified and complete theory of turbulence has not yet been established. Most scholars believe that turbulence should be studied from the Naville-Stokes equation. Turbulence is extremely important for many important scientific and technological problems.

Therefore, the practice adopted in recent decades is to establish a concrete mechanical model suitable for specific kinds of phenomena. For example, the turbulence model is only applicable to the appendage flow; Only suitable for the process of simple detachment and reattachment; It is only suitable for airfoil wake or turbulence model of interaction between shock wave and boundary layer.