Замыкание уравнений Рейнольдса для устойчиво стратифицированных турбулентных течений в атмосфере и океане

Авторы: Зилитинкевич С.С., Эльперин Т., Клиорин Н., Рогачевский И.

Год: 2009

Номер: 04

Страницы: 75-102

Аннотация

Предлагается модель замыкания уравнений Рейнольдса, основанная на уравнениях баланса для фундаментальных вторых моментов: ТКЭ (турбулентной кинетической энергии) и ТПЭ (турбулентной потенциальной энергии), вместе составляющих полную или суммарную энергию турбулентности: СЭТ=ТКЭ+ТПЭ, а также вертикальных турбулентных потоков импульса и плавучести (пропорциональной потенциальной температуре). Кроме понятия СЭТ, наш подход содержит ещё два новых ключевых элемента: неградиентную поправку к потоку плавучести и зависимость анизотропии поля скоростей от стратификации течения. В предложенной модели гарантирована возможность существования турбулентности при любом градиентном числе Ричардсона, Ri. Вместо критического значения числа Ричардсона, которое разделяет – как обычно предполагается – турбулентный и ламинарный режимы, в предлагаемой модели появляется переходный интервал, 0.1<Ri <1  , разделяющий два режима существенно различной природы: сильная турбулентность обычного типа при Ri«1; и слабая турбулентность, способная переносить импульс, но намного менее эффективная в переносе тепла, при Ri>1. Расчеты по нашей модели согласуются с данными атмосферных и лабораторных экспериментов, полного вихреразрешающего численного моделирования турбулентности (direct numerical simulation = DNS) и частично вихреразрешающего моделирования турбулентности (large-eddy simulation = LES).

Теги: анизотропия; замыкание уравнений турбулентного движения; кинетическая энергия турбулентности; критическое число Ричардсона; полная энергия турбулентности; потенциальная энергия турбулентности; путь смешения; турбулентная вязкость; турбулентный перенос; устойчивая стратификация

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