Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature

Nabiyeva, I, Juraboyeva, O, Набиева, И, Джурабоева, O, Nabiyeva, I, Juraboyeva, O

Mexanika muammolari jurnali · 2026-yil

Annotatsiya

A three-dimensional model is developed for the dispersion of harmful substances in the atmospheric surface layer with allowance for the spatial–temporal variation of temperature. The advection–diffusion equation for the pollutant, written in conservative form with a temperature-dependent gravitational-settling flux, is solved together with a temperature (energy) equation; the dynamic viscosity (Suther- land’s law), the air density, the molecular diffusivity and the settling velocity are functions of the local temperature, and the atmospheric thermal stability enters the vertical turbulent diffusion through the gradient Richardson number and a monotone stability function. The problem is discretised by an explicit finite-volume scheme with upwind advection and a combined Courant–Friedrichs–Lewy step, point sources are prescribed as grid-independent mass rates, and the ground boundary is treated as dry deposition with a tracked deposited mass. The scheme is validated against an analytical Gaussian solution and verified by machine-precision mass conservation and grid/time convergence. Two reproducible regimes are computed: a daytime unstable case (???????? < 0) and a night-time surface inversion (???????? > 0). Under the inversion the vertical mixing is suppressed by more than an order of magnitude, the pollutant is confined to a shallow near-surface layer with an in-layer peak about three times the daytime value, and only about 18% of the emitted mass is ventilated out of the region against about 70% in the daytime. The example is illustrative rather than a site-specific prediction.

Maqola ma’lumotlari
MualliflarNabiyeva, I, Juraboyeva, O, Набиева, И, Джурабоева, O, Nabiyeva, I, Juraboyeva, O
JurnalMexanika muammolari jurnali
NashriyotМеханика ва иншоотлар сейсмик мустаҳкамлиги институти
ISSN2010-7250
Nashr sanasi2026-10-14
Jild37
Son3
Betlar99-105
TilIngliz
Ilmiy sohaFizika-matematika
Indeksga qo‘shilgan2026-10-18

Maqolaning asl sahifasi

Kalit so‘zlar

advection-diffusion equation, temperature inversion, thermal stability, Richardson number, gravitational settling, finite-volume method, mass conservation, уравнение адвекции–диффузии, температурная инверсия, термическая устойчивость, число Ричардсона, гравитационное осаждение, метод конечных объёмов, сохранение массы, adveksiya–diffuziya tenglamasi, harorat inversiyasi, termik barqarorlik, Richardson soni, gravitatsion cho‘kish, chekli hajmlar usuli, massaning saqlanishi

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APANabiyeva, I, Juraboyeva, O, Набиева, И, Джурабоева, O, Nabiyeva, I, & Juraboyeva, O (2026). Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature. Mexanika muammolari jurnali, 37(3), 99-105. https://www.pmjournal.uz/index/article/view/29
GOST (OAK)Nabiyeva, I va b. Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature // Mexanika muammolari jurnali. – 2026. – T. 37, № 3. – P. 99-105.
MLANabiyeva, I, Juraboyeva, O, Набиева, И, Джурабоева, O, Nabiyeva, I, and Juraboyeva, O. “Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature.” Mexanika muammolari jurnali, 37(3), 99-105, 2026. https://www.pmjournal.uz/index/article/view/29
ChicagoNabiyeva, I, Juraboyeva, O, Набиева, И, Джурабоева, O, Nabiyeva, I, and Juraboyeva, O. “Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature.” Mexanika muammolari jurnali, 37(3), 99-105 (2026). https://www.pmjournal.uz/index/article/view/29
HarvardNabiyeva, I, Juraboyeva, O, Набиева, И, Джурабоева, O, Nabiyeva, I, and Juraboyeva, O (2026) ‘Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature’, Mexanika muammolari jurnali, 37(3), 99-105. https://www.pmjournal.uz/index/article/view/29
BibTeX
@article{nabiyevai2026,
  title = {Mathematical modelling of pollutant dispersion in the atmosphere with allowance for the spatial--temporal variation of temperature},
  author = {Nabiyeva, I and Juraboyeva, O and Набиева, И and Джурабоева, O and Nabiyeva, I and Juraboyeva, O},
  journal = {Mexanika muammolari jurnali},
  year = {2026},
  volume = {37},
  number = {3},
  pages = {99-105},
  url = {https://www.pmjournal.uz/index/article/view/29}
}

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