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Nonlinear interactions in turbulence with strong irrotational straining. (English) Zbl 0892.76037
The rate of growth of the nonlinear terms in the vorticity equation are analyzed for a turbulent flow with r.m.s. velocity \(u_0\) and integral length scale \(L\) subjected to a strong uniform irrotational plane strain \(S\), where \((u_0/L)/S= \varepsilon\ll 1\). The rapid distortion theory (RDT) solution is the zeroth-order term of the perturbation series solution in terms of \(\varepsilon\). We use the asymptotic form of the convolution integrals for the leading-order nonlinear terms when \(\beta= \exp(-St)\ll 1\) to determine at what time \(t\) and beyond what wavenumber \(k\) (normalized on \(L\)) the perturbation series in \(\varepsilon\) fails, and hence derive conditions for the validity of RDT in these flows.

MSC:
76F10 Shear flows and turbulence
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