Physics. Visualizing the dynamics of the onset of turbulence

Kinetic energy is the ability of an object in motion to do work or enact change. It can take on many forms. For instance, water flowing down a waterfall has kinetic energy. In biological systems, particles of light travel and are absorbed by plants to create chemical energy. Animals consume the chemical energy and give off molecules that carry their scent through the air. They also generate kinetic energy when they run away from predators. Entire systems also possess kinetic energy, like the...

Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the streamlines...

When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
The SI unit of viscosity is...

Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...

Viscosity is a property of fluids that measures their resistance to flow. It is influenced by factors such as the surface area of contact, the gradient of flow speed, and the fluid's viscosity constant, called the coefficient of viscosity. The coefficient of viscosity, also known as dynamic viscosity, is denoted by the symbol η. It determines the proportionality between the viscous force and the gradient of flow speed.Newton's law of viscosity states that the viscous force on a faster-moving...

A streamline represents the trajectory that is always tangent to the fluid's velocity vector at any given point. The velocity of a fluid particle is always directed along the streamline, ensuring the particle continuously follows the streamline's path. Streamlines are particularly useful for visualizing the overall direction of flow in a fluid system, and they provide an instantaneous representation of the flow's velocity field. In steady flow, where conditions do not change over time,...