Effective Diffusivity in Baroclinic Flow
Large-scale chaotic stirring stretches tracer contours into filaments containing fine spatial scales until small-scale diffusive processes dissipate tracer variance. Quantification of tracer transport in such circumstances is possible through the use of Nakamura’s “effective diffusivity” diagnostics...
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| Format: | Article |
| Language: | en_US |
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American Meteorological Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/91278 https://orcid.org/0000-0002-6716-1576 |
| _version_ | 1811095005156081664 |
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| author | Plumb, R. Alan Leibensperger, Eric Michael |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Plumb, R. Alan Leibensperger, Eric Michael |
| author_sort | Plumb, R. Alan |
| collection | MIT |
| description | Large-scale chaotic stirring stretches tracer contours into filaments containing fine spatial scales until small-scale diffusive processes dissipate tracer variance. Quantification of tracer transport in such circumstances is possible through the use of Nakamura’s “effective diffusivity” diagnostics, which make clear the controlling role of stirring, rather than small-scale dissipation, in large-scale transport. Existing theory of effective diffusivity is based on a layerwise approach, in which tracer variance is presumed to cascade via horizontal (or isentropic) stirring to small-scale horizontal (or isentropic) diffusion. In most geophysical flows of interest, however, baroclinic shear will tilt stirred filamentary structures into almost-horizontal sheets, in which case the thinnest dimension is vertical; accordingly, it will be vertical (or diabatic) diffusion that provides the ultimate dissipation of variance. Here new theoretical developments define effective diffusivity in such flows. In the frequently relevant case of isentropic stirring, it is shown that the theory is, in most respects, unchanged from the case of isentropic diffusion: effective isentropic diffusivity is controlled by the isentropic stirring and, it is argued, largely independent of the nature of the ultimate dissipation. Diabatic diffusion is not amplified by the stirring, although it can be modestly enhanced through eddy modulation of static stability. These characteristics are illustrated in numerical simulations of a stratospheric flow; in regions of strong stirring, the theoretical predictions are well supported, but agreement is less good where stirring is weaker. |
| first_indexed | 2024-09-23T16:09:01Z |
| format | Article |
| id | mit-1721.1/91278 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:09:01Z |
| publishDate | 2014 |
| publisher | American Meteorological Society |
| record_format | dspace |
| spelling | mit-1721.1/912782024-05-15T08:25:13Z Effective Diffusivity in Baroclinic Flow Plumb, R. Alan Leibensperger, Eric Michael Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Plumb, R. Alan Leibensperger, Eric M. Large-scale chaotic stirring stretches tracer contours into filaments containing fine spatial scales until small-scale diffusive processes dissipate tracer variance. Quantification of tracer transport in such circumstances is possible through the use of Nakamura’s “effective diffusivity” diagnostics, which make clear the controlling role of stirring, rather than small-scale dissipation, in large-scale transport. Existing theory of effective diffusivity is based on a layerwise approach, in which tracer variance is presumed to cascade via horizontal (or isentropic) stirring to small-scale horizontal (or isentropic) diffusion. In most geophysical flows of interest, however, baroclinic shear will tilt stirred filamentary structures into almost-horizontal sheets, in which case the thinnest dimension is vertical; accordingly, it will be vertical (or diabatic) diffusion that provides the ultimate dissipation of variance. Here new theoretical developments define effective diffusivity in such flows. In the frequently relevant case of isentropic stirring, it is shown that the theory is, in most respects, unchanged from the case of isentropic diffusion: effective isentropic diffusivity is controlled by the isentropic stirring and, it is argued, largely independent of the nature of the ultimate dissipation. Diabatic diffusion is not amplified by the stirring, although it can be modestly enhanced through eddy modulation of static stability. These characteristics are illustrated in numerical simulations of a stratospheric flow; in regions of strong stirring, the theoretical predictions are well supported, but agreement is less good where stirring is weaker. National Science Foundation (U.S.) (Grant ATM-0852384) 2014-11-04T13:51:23Z 2014-11-04T13:51:23Z 2014-03 2013-11 Article http://purl.org/eprint/type/JournalArticle 0022-4928 1520-0469 http://hdl.handle.net/1721.1/91278 Leibensperger, Eric M., and R. Alan Plumb. “Effective Diffusivity in Baroclinic Flow.” J. Atmos. Sci. 71, no. 3 (March 2014): 972–984. © 2014 American Meteorological Society https://orcid.org/0000-0002-6716-1576 en_US http://dx.doi.org/10.1175/JAS-D-13-0217.1 Journal of the Atmospheric Sciences Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Meteorological Society American Meteorological Society |
| spellingShingle | Plumb, R. Alan Leibensperger, Eric Michael Effective Diffusivity in Baroclinic Flow |
| title | Effective Diffusivity in Baroclinic Flow |
| title_full | Effective Diffusivity in Baroclinic Flow |
| title_fullStr | Effective Diffusivity in Baroclinic Flow |
| title_full_unstemmed | Effective Diffusivity in Baroclinic Flow |
| title_short | Effective Diffusivity in Baroclinic Flow |
| title_sort | effective diffusivity in baroclinic flow |
| url | http://hdl.handle.net/1721.1/91278 https://orcid.org/0000-0002-6716-1576 |
| work_keys_str_mv | AT plumbralan effectivediffusivityinbaroclinicflow AT leibenspergerericmichael effectivediffusivityinbaroclinicflow |