Fundamentals of Turbulence Flow
2.2 SINGLE-PHASE FLUID FLOW
2.2.1 Introduction and fundamentals
2.2.1.3 Fundamentals of turbulence flow
K. Gersten
A. Conservation equations for turbulent flows
Most flows that occur in practical applications are turbulent. The main characteristic feature of turbulent flow is the irregular fluctuation of all variables which is superimposed on the mean values. The instantaneous quantities of turbulent flow are replaced by their mean and by their fluctuating quantities. If f (r, t) is a typical flow quantity, we may write:
\[\label{eq1} f(r,\;t)=\tilde{f}(r)+f^{\prime}(r,\;t)=\bar{f}(r)+f^{\prime\prime}(r,\;t) \tag{1}\]
Here, two different ways of averaging appear; the time average,
\[\label{eq2} \bar{f}(r)=\frac{1}{\varDelta t}\int_{t_0}^{t_0+\varDelta t}\!{f(r,t)\,dt} \tag{2}\]
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