- #1
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There is one point in my book, where I am confused about the notation. In index notation the equation is:
dai = aj∇j ui
In matrix notation I would write this as:
da = (a⋅∇)u
where the term in the parenthis is just a scalar or if you will the unit matrix multiplied by a scalar.
But my book rewrites this as:
da = a ⋅ ∇u (1)
where the latter is a matrix of gradients with elements Aij = ∇jui
I don't understand this last rewriting. If you choose to use this matrix of gradients shouldn't it be:
da = (∇u)a
Or maybe I'm misinterpreting (1). Isn't a in this case a row vector and the matrix of displacement gradients has for example on the first row: ∇xux,∇yux ,∇zux. I would like it to be transposed to make meaning of the above.
dai = aj∇j ui
In matrix notation I would write this as:
da = (a⋅∇)u
where the term in the parenthis is just a scalar or if you will the unit matrix multiplied by a scalar.
But my book rewrites this as:
da = a ⋅ ∇u (1)
where the latter is a matrix of gradients with elements Aij = ∇jui
I don't understand this last rewriting. If you choose to use this matrix of gradients shouldn't it be:
da = (∇u)a
Or maybe I'm misinterpreting (1). Isn't a in this case a row vector and the matrix of displacement gradients has for example on the first row: ∇xux,∇yux ,∇zux. I would like it to be transposed to make meaning of the above.