A novel technique for experimental modal analysis of barotropic seiches for assessing lake energetics

Abstract

Basin scale seiches in lakes are important elements of the total energy budget and are a driver of fluxes of important ecological parameters, such as oxygen, nutrients, and sediments. At present, the extraction of the damping ratios of surface seiches, which are directly related to the capacity of seiches to drive these fluxes through the increased mixing of the water column, is reliant on spectral analysis which may be heavily influenced by the transformation of water level records from the time domain to the frequency domain, and which are sensitive to the level of noise present within the data. Existing spectral-based methods struggle to extract the periods of surface seiches which are of similar magnitude due to the overlap between their spectral responses. In this study, the principles of operational modal analysis, through the random decrement technique (RDT), currently used primarily in the analysis of high rise structures and in the aeronautical industry and not previously applied within the fields of limnology or ecology, are applied to barotropic seiches through the analysis of water level data for Lake Geneva, Switzerland, and Lake Tahoe, USA. Using this technique, the autocorrelation of the measurements is estimated using the RDT and modal analysis can then be carried out on this time-domain signal to estimate periods of the dominant surface seiches and the corresponding damping ratios. The estimated periods show good agreement with experimental results obtained through conventional spectral techniques and consistent damping ratios are obtained for the dominant surface seiche of Lake Tahoe. The effect of input parameters is discussed, using data for the two lakes, alongside discussion of the application of RDT to the study of internal seiches and current barriers to its application. RDT has great potential for the analysis of both surface and internal seiches, offering a method through which accurate damping ratios of seiche oscillations may be obtained using readily available data without necessitating spectral analysis.

Laboratory experiments on the influence of stratification and a bottom sill on seiche damping

“…The coupling between barotropic tidal waves at the sea surface and internal gravity waves facilitates heat and material exchange between the uppermost and deeper layers (Garrett, 2003;Lelong and Kunze, 2013;Morozov, 2018;Vic et al, 2019;Rippeth and Green, 2020;Stanev and Ricker, 2020). This largely interconnected dynamic is particularly pertinent in semi-enclosed basins, bays, and fjords with density profiles characterized by sharp gra-dients (Rattray, 1960;Niiler, 1968;Bell, 1975;Stigebrandt, 1980;Stigebrandt and Aure, 1989;Chapman and Giese, 1990;Münnich, 1996;Parsmar and Stigebrandt, 1997;Stigebrandt, 1999;Imberger, 2001, 2003;Inall et al, 2004;Cushman-Roisin et al, 2005;Johnsson et al, 2007;Boegman and Ivey, 2012;Park et al, 2016;Staalstrøm and Røed, 2016;Castillo et al, 2017;Roget et al, 2017;Stanev and Ricker, 2020;Xue et al, 2020).…”

“…However, in semi-enclosed systems the surface seiche period was found to be more sensitive to the stratification. This effect of internal wave excitation on the decay of surface seiches was further investigated by Wynne et al (2019). When the characteristic (e.g., diurnal) frequency of the wind forcing matches that of a seiche eigenmode, a resonant amplification of the latter may occur.…”

“…They modeled resonant barotropic-baroclinic energy conversion of a periodically forced shallow water system in a rectangular tank without topographic obstacles in order to quantify the energy flux pathways between the applied forcing and the internal wave field. A similar setting (i.e., a rectangular tank with a flat bottom) has also been studied recently by Xue et al (2020), with a special focus on internal wave excitation and seiche damping. Similar laboratory models can provide illuminating results for the interpretation of direct oceanic observations because they make it possible to focus on specific phenomena that are inevitably loaded with disturbing effects in natural environments.…”

Laboratory experiments on the influence of stratification and a bottom sill on seiche damping

“…However, in semi-enclosed systems, such as bays, where freely propagating internal waves can "radiate" away, into the open ocean, the surface seiche period was found to be more sensitive to the stratification. This effect of internal wave excitation on the decay of surface seiches was further investigated by Wynne et al (2019).…”

Experimental Analysis of Waves in Environmental Flows

“…However, in semi-enclosed systems the surface seiche period was found to be more sensitive to the stratification. This effect of internal wave excitation on the decay of surface seiches was further investigated by [71]. When the characteristic (e.g.…”