Question

Consider a vector flow variable which can be decomposed as \(\vec{a}=\vec{A}+\vec{a’}.\overline{div \,\vec{a}}\) will be equal to ____________

(a) div \(\vec{A}\)

(b) \(\overline{div \vec{a’}}\)

(c) \(\overline{div \vec{a}}\)

(d) \(\overline{div \vec{A}}\)

The question was asked in exam.

My doubt is from Turbulence Modelling in chapter Turbulence Modelling of Computational Fluid Dynamics

Answer 1

The correct answer is (a) div \(\vec{A}\)

To explain: From the given problem,

\(\overline{div \,\vec{a}}=div\overline{\vec{a}}=div\overline{\vec{A}+\vec{a’}} = div\overline{\vec{A}}=div\vec{A}\).