Quantification of energy cascade of internal gravity waves with varying spectral slopes

海洋的垂直密度差异支持具有不同周期的“内部”波（海洋内部的波）。这些内部波的能量通常会滴入较小的波中，最终消散，这一过程被称为能量级联。级联过程可以导致混合，并决定热量和盐的平衡以及海洋的总体环流。该项目将通过理论、建模和数据分析来研究这种能量级联。现有的基于内波产生湍流的能量级联理论将在本研究中得到完善（解决了现有的争议），并将其推广到更现实的情况。改进理论的后续验证将通过高分辨率区域模式模拟来完成。该项目还将把这一改进的理论应用于全球模式模拟，并建立耗散的地理地图。更广泛的影响包括增强全球气候模式和区域模式。理论上的改进将为内波湍流的一系列物理应用和数学研究提供信息。计划为湍流社区做年度报告。这项工作支持了早期职业生涯的PI，博士后，通过加纳沿海海洋环境暑期学校的教学和公共宣传，以及通过UM自然历史博物馆的项目进行的流体力学历史公开讲座。该项目将从理论和计算两个方面全面了解具有可变光谱斜率的IGW光谱的小尺度能量级联。研究任务包括：1)在波动湍流理论框架下，建立变斜率谱能量级联的理论公式，并通过动力学方程的模拟来指导和验证。2)进一步改进24-32°N， 193-199°E区域的MITgcm模拟（通过调整模式分辨率和k -廓线参数化），以更好地匹配McLane剖面仪测量的光谱，计算模型能量级联并与任务1的理论结果进行比较。3)应用传统/新型细尺度参数化方法建立全球MITgcm模型湍流耗散率的地理分布图，并与微结构测量结果进行比较。新的精细尺度参数化公式更接近于测量光谱，加上通过调整k线参数化改进的区域模式，将从根本上改善海洋模式中的双周期混合参数化。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Vertical density differences in the ocean support 'internal' waves (waves in the ocean's interior) that have different periods. The energy of these internal waves often trickles down to smaller waves that eventually dissipate, a process known as the energy cascade. The cascade process can lead to mixing, and determines the heat and salt balances and general circulation of the ocean. This project will investigate this energy cascade through theory, modeling, and data analysis. The existing theory of the energy cascade, based on the turbulence produced by internal waves, will be improved in this study (with existing controversies resolved) and extended to more realistic situations. Subsequent validation of the improved theory will be done with high-resolution regional model simulations. The project will also apply this improved theory to a global model simulation and establish a geographic map of dissipation . Broader impacts include enhancements to global climate models and regional models. The theoretical improvement will inform a range of physical applications and mathematical studies of internal wave turbulence. Annual presentations are planned for the turbulence community. The work supports an early career PI, a postdoc, and teaching and public outreach through the Coastal Ocean Environment Summer School in Ghana and public lectures on the history of fluid mechanics through programs at the UM Museum of Natural History.The proposed project will establish a comprehensive understanding of the downscale energy cascade of IGW spectra with variable spectral slopes, from both theoretical and computational considerations. Research tasks include: 1) Development of theoretical formulations of energy cascade for spectra with varying slopes in the wave turbulence theory framework, which will be guided and confirmed by simulations of the kinetic equation. 2) Further improvement of the regional MITgcm simulation of 24-32 degrees N, 193-199 degrees E to better match the spectra from McLane profiler measurements (through adjustment of model resolution and K-profile parameterization), computation of the modeled energy cascade with comparison to theoretical results obtained from task 1. 3) Application of the traditional/new finescale parameterization to a global MITgcm model to establish a geographic map of turbulent dissipation rate, and comparison of the results to those from microstructure measurements. The new finescale parameterization formulation from spectra that more closely match spectra from measurements, together with improved regional models through tuning of K-profile parameterization, will lead to fundamentally improved diapycnal mixing parameterizations in ocean models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.