Tensor Derivative (continuum Mechanics) - Divergence of A Tensor Field

Divergence of A Tensor Field

The divergence of a tensor field is defined using the recursive relation

(\boldsymbol{\nabla}\cdot\boldsymbol{T})\cdot\mathbf{c} = \boldsymbol{\nabla}\cdot(\mathbf{c}\cdot\boldsymbol{T}) ~;\qquad\boldsymbol{\nabla}\cdot\mathbf{v} = \text{tr}(\boldsymbol{\nabla}\mathbf{v})

where c is an arbitrary constant vector and v is a vector field. If is a tensor field of order n > 1 then the divergence of the field is a tensor of order n−1.

Read more about this topic:  Tensor Derivative (continuum Mechanics)

Famous quotes containing the word field:

    “How sweet I roam’d from field to field
    And tasted all the summer’s pride,
    Till I the Prince of Love beheld
    Who in the sunny beams did glide!”
    —William Blake (1757–1827)