(u(boldsymbol{x}, t)) and (v(boldsymbol{x}, t)) are velocity components of a turbulent flow. The RANS averaging (langle v(a...

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\(u(\boldsymbol{x}, t)\) and \(v(\boldsymbol{x}, t)\) are velocity components of a turbulent flow. The RANS averaging \(\langle v(a u+b)angle\) is evaluated, where \(a\) and \(b\) are some constants. Rewrite the expression in the RANS form. i.e. as a sum of the terms containing \(\langle uangle\) and \(\langle vangle\) and the irreducable terms containing the averages of the products of the fluctuations \(u^{\prime}\) and \(v^{\prime}\).

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