Evanescent to propagating internal waves in experiments, simulations, and linear theory
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RESEARCH ARTICLE
Evanescent to propagating internal waves in experiments, simulations, and linear theory Allison Lee1 · Kyle Hakes2 · Yuxuan Liu3 · Michael R. Allshouse3 · Julie Crockett2 Received: 1 November 2019 / Revised: 14 October 2020 / Accepted: 15 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Experiments, numerical simulations, and linear theory are used to explore the kinetic energy density of waves generated by oscillating topography in a nonlinear stratification. Initially, generated waves are evanescent but then pass through a turning depth and into a propagating region. A technique for calculating kinetic energy density indirectly via the density perturbation field measured using synthetic schlieren is tested to assess the validity of the calculation. To establish the indirect calculation’s range of validity, numerical simulations were performed to compare the indirect calculation to an estimate of kinetic energy calculated from local velocity components (referred to here as the standard calculation). In addition, the standard calculation is applied to the velocity field determined via linear theory, which defines the fluid velocity using similar assumptions to the indirect calculation of kinetic energy. Both calculation methods show similar trends in the average kinetic energy density present in propagating waves as a function of Froude number, topography height, and distance from topography to the turning depth. Local comparisons of kinetic energy density from the indirect and standard calculations identify regions where the two methods compare well. Additionally, a correlation between linear theory and numerical simulations is presented to evaluate the range of applicability of the linear theory. Keywords Stratified flows · internal waves · variable stratifications
1 Introduction Internal waves, which form in stratified mediums such as the ocean and atmosphere, impact climate, weather, ocean circulation and the global energy budget of the ocean (Garret and Munk 1979; Fritts 1984; Garrett and Kunze 2007; Sutherland 2010). To better understand the influence of internal waves, researchers employ a variety of methods to study atmospheric and oceanic waves including observations, theoretical analysis, numerical simulations, and laboratory experiments. Each method can provide a wide variety of data that leads to insight on how internal waves transfer energy can affect mixing in the atmosphere and ocean (Garrett and Kunze 2007; Sarkar and Scotti 2017; Sutherland et al. 2019). However, each method has its own limitations and * Julie Crockett [email protected] 1
Campbell University, Buies Creek, USA
2
Brigham Young University, Provo, USA
3
Northeastern University, Boston, USA
researchers must choose a method to study internal waves based on the complexity of the phenomena being studied and the resources available. One mechanism of internal wave generation occurs when tidally generated evanescent waves in the deep ocean pass through a turning dept
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