1999
DOI: 10.1063/1.869967
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An anelastic, scale-separated model for mixing, with application to atmospheric transport phenomena

Abstract: We present and analyze a simpli ed, scale-separated, anelastic uid model which is designed to assess the in uence of weak compressibility in the di usive transport of a passive scalar. Our model incorporates a slowly varying, density induced, anisotropy into a xed, rapidly varying (small scale) uid ow. This anisotropy is physically motivated through the anelastic mass balance which retains vertical density variations occurring over the atmospheric scale height (8 km). Consequently, these steady ows are non-sol… Show more

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Cited by 13 publications
(9 citation statements)
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“…To this end, we simulate this complete anelastic system for four different Prandtl numbers (P r = 10, 1, .1, .01) and exhibit how this particular blocking event arises in the low Prandtl number limit. We remark that this phenomenon is similar in spirit with existing compressible passive scalar studies [9,10] designed to assess the role of a structured density profile in modifying vertical transport; however, the present case involves fully nonlinear, dynamic simulations.…”
Section: Introductionsupporting
confidence: 59%
See 1 more Smart Citation
“…To this end, we simulate this complete anelastic system for four different Prandtl numbers (P r = 10, 1, .1, .01) and exhibit how this particular blocking event arises in the low Prandtl number limit. We remark that this phenomenon is similar in spirit with existing compressible passive scalar studies [9,10] designed to assess the role of a structured density profile in modifying vertical transport; however, the present case involves fully nonlinear, dynamic simulations.…”
Section: Introductionsupporting
confidence: 59%
“…In the context of scalar mixing, McLaughlin and Forest [9] have demonstrated using methods of homogenized averaging that idealized (small scale, weakly compressible) anelastic flows involving a structured background density field yield quite different effective mixing properties than their incompressible counterpart. Specifically, the presence of a density transition layer, such as that found in many boundary layers, may lead to anisotropic effective diffusion arising in the form of local regions of trapped and focused contaminants near the transition height.…”
Section: Introductionmentioning
confidence: 99%
“…This is consistent with what has been observed in geophysical flows in the climate system, as discussed above. In [62], this result was extended to weakly compressible, anelastic fluid velocity fields.…”
mentioning
confidence: 89%
“…The mathematical framework developed in [61] was adapted [75,62,57] to the case of a periodic, time-dependent, incompressible fluid velocity field with non-zero mean. The velocity field was modeled as a superposition of a large-scale mean flow with small-scale periodically oscillating fluctuations.…”
mentioning
confidence: 99%
“…The velocity-dependent dispersion is usually modeled by a nonlinear tensor which is of the form (see [37]) E(q) = <t> (d m ld + \q\ (d L £(q) + dr(ldwhere £(q)ij = qiqj/\q\ 2 , the real d m is the molecular diffusion, di and dj-are the longitudinal and transverse dispersion constants. However we emphasise that this work remains true for other settings: for more complex diffusion tensors containing effective drift correction (see for instance [8, 3 3 , 2]), or in presence of turbulent diffusive effects (see [10,7] for oceanic turbulent flows, [30] for atmospheric transport problems, [41] for bio-turbulent flows). See also [40] and the references therein for problems of dispersion in fixed beds.…”
Section: H(c)mentioning
confidence: 99%