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• W3100302885 abstract "We consider a class of invariant measures for a passive scalar $f$ driven by an incompressible velocity field $boldsymbol{u}$, on a $d$-dimensional periodic domain, satisfying $$ partial_t f + boldsymbol{u} cdot nabla f = 0, qquad f(0)=f_0. $$ The measures are obtained as limits of stochastic viscous perturbations. We prove that the span of the $H^1$ eigenfunctions of the operator $boldsymbol{u}cdotnabla$ contains the support of these measures. We also analyze several explicit examples: when $boldsymbol{u}$ is a shear flow or a relaxation enhancing flow (a generalization of weakly mixing), we can characterize the limiting measure uniquely and compute its covariance structure. We also consider the case of two-dimensional cellular flows, for which further regularity properties of the functions in the support of the measure can be deduced. The main results are proved with the use of spectral theory results, in particular the RAGE theorem, which are used to characterize large classes of orbits of the inviscid problem that are growing in $H^1$." @default.
• W3100302885 created "2020-11-23" @default.
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• W3100302885 date "2016-09-22" @default.
• W3100302885 modified "2023-09-30" @default.
• W3100302885 title "Invariant Measures for Passive Scalars in the Small Noise Inviscid Limit" @default.
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• W3100302885 doi "https://doi.org/10.1007/s00220-016-2758-9" @default.
• W3100302885 hasPublicationYear "2016" @default.
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