Free surface

A free surface is a concept used in fluid dynamics to describe a fluid interface that is subject to zero parallel shear stress, such as the boundary between two homogeneous fluids, for example, liquid and gas (like water and air), or between a liquid and a vacuum. The term is also applied to the interface between liquid and a solid if the solid is completely submerged in the liquid and there is no contact angle (meaning the angle between the solid surface and the tangent to the liquid surface at the point of contact is 90 degrees).

In the context of fluid mechanics, understanding the behavior of a free surface is crucial for predicting how liquids will act in various situations, such as in the design of watercraft, the study of waves on the ocean, the flow of water in rivers and canals, and in the containment of liquids in tanks and reservoirs. The dynamics of free surfaces are complex and influenced by factors such as gravity, surface tension, and viscosity.

The mathematical modeling of free surface flows is a challenging area of fluid dynamics due to the difficulty in predicting the shape and movement of the surface boundary. The Navier-Stokes equations, which describe the motion of viscous fluid substances, are often used in these models, but solving these equations for free surface flows requires sophisticated numerical techniques and assumptions.

One common assumption in the study of free surfaces is the ideal fluid assumption, where the fluid is considered to be incompressible and inviscid (having no viscosity). This simplification can make the mathematical analysis more manageable but may not always accurately reflect real-world conditions.