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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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