Bounded dissipation law and profiles of turbulent velocity moments in wall flows

• 成果类型: Article
• 署名作者: Chen, Xi; Sreenivasan, Katepalli R.
• 署名单位: Beihang University; New York University; New York University Tandon School of Engineering
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-11486
• DOI: 10.1073/pnas.2502265122
• 发表日期: 2025-04-29
• 关键词: direct numerical-simulation

摘要

Understanding the effects of solid boundaries on turbulent fluctuations remains a longstanding challenge. Available data on mean-square fluctuations in these flows show apparent contradiction with classical scaling. We had earlier proposed an alternative model based on the principle of bounded dissipation. Despite its putative success, a conclusive outcome requires much higher Reynolds numbers than are available at present, or can be expected to be available in the near future. However, the model can be validated satisfactorily even within the Reynolds number range already available by considering high-order moments and their distributions in the wall-normal direction. Expressions for high-order moments of streamwise velocity fluctuation u are derived in the form (u(+2q))(1/q) = alpha(q) - beta(*1/4)(qy), where the superscript + indicates the wall unit normalization, and brackets stand for averages over time and the homogeneous plane normal to the wall, q is an integer, alpha(q) and beta(q) are constants independent of the friction Reynolds number Re-tau, and y* = y/delta is the distance away from the wall, normalized by the flow thickness S. In particular,alpha(q)= mu + sigma q according to the linear q-norm Gaussian process, where mu and r are flow-independent constants. Excellent agreement is found between this formula and the available data in boundary layers, pipes, and channels for 1 <= q <= 5. For fixed y(+) = y*Re-tau, the present formulation leads to the bounded state (u(+2q))(1/q) = alpha(q) as Re-tau -> infinity. This work demonstrates the success of the present model in describing the behavior of fluctuations in wall flows.