Statistical Analysis of the Limiting Dynamics of Two dimensional Boussinesq Turbulent Systems

Technical Report · Tue Dec 05 04:00:00 EST 2023

DOI:https://doi.org/10.2172/2229651· OSTI ID:2229651

Xie, Xuping ^[1]; Majda, Andrew J. ^[2]; Qi, Di ^[3]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. New York Univ. (NYU), NY (United States)
3. Purdue Univ., West Lafayette, IN (United States)

In the current study, we investigate rotational and stratified turbulent systems within the framework of the Boussinesq equations. The effects of rotation and stratification give rise to a variety of dynamical regimes in atmospheric and oceanic turbulence. To develop a better understanding of the fundamental flow properties through a more straightforward mathematical framework, we commence our research with a simplified two-dimensional Boussinesq model that incorporates rotation and stratification effects. We explore two distinct limiting dynamics, considering pure rotation and pure stratification separately. We examine these intriguing dynamics through numerical investigations, applying the exact solution theory of Boussinesq equations and examining small-scale perturbations to the exact solution under rotation and stratification. We conduct an analysis of statistical quantities associated with the turbulent state variables. The results indicate that, under weak rotation at the equilibrium statistical state, the flow field exhibits vortex flow. However, strong rotation transforms the flow into vertical shear flow. We observe both downscale and upscale energy transfers with a decay rate of k⁻³ in the absence of external forcing and dissipation. Furthermore, we delve into the study of internal gravity wave mode interactions in the simplified two-dimensional Boussinesq system, which is a crucial aspect of geophysical turbulence due to gravity. Our findings reveal that the time series of the mode coefficients exhibit wave-like interactions between wave modes.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: 89233218CNA000001
• OSTI ID: 2229651
• Report Number(s): LA-UR--23-33566
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
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Stratification Turbulence