What is a traceless tensor?

Traceless Tensors. Tensors T with zero trace, i.e. ( ) ∑ , are called traceless.

What is called tensor?

Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor.

What is a second order tensor?

Second order tensors are the next, requiring magnitude and two directions/indices to specify. The most common example of this, which is also taught in engineering, are the stress and strain tensors.

What is quotient law in tensor?

A.1.3 The Quotient Law. A set of 3r numbers form the components of a tensor of rank r, if and only if its scalar product with another arbitrary tensor is again a tensor. This is called the quotient law and can be used as a litmus test whether a set of numbers form a tensor.

What is the difference between circulation and vorticity?

• Circulation and vorticity are the two primary measures of rotation in a fluid. • Circulation, which is a scalar integral quantity, is a macroscopic measure of rotation for a finite area of the fluid. • Vorticity, however, is a vector field that gives a microscopic measure of the rotation at any point in the fluid.

What is the strength of the vorticity of a vortex line?

Figure 7.2.1 A vortex line It is important to note that the strength of the vector vorticity is not constant along a vortex line in the same way that the velocity is not (necessarily) constant along a streamline. A vortex tubeis a cylindrical tube in space whose surface elements are composed of

What is the vorticity of the fluid element moving from a to B?

Figure 7.1.1 The fluid element moving from A to B on a circular path has no vorticity while the fluid element moving from C to D has vorticity. It is important to keep in mind the distinction between vorticity and the curvature of streamlines. A B C D Chapter 7 3 7.2 Vortex lines and tubes.

What is the stress tensor in fluid mechanics?

A key step in formulating the equations of motion for a fluid requires specifying the stress tensor in terms of the properties of the flow, in particular the velocity field, so that the theory becomes “closed”, that is, that the number of variables is reduced to the number of governing equations.