An empirical parametrization of internal seiche amplitude including secondary effects
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An empirical parametrization of internal seiche amplitude including secondary effects Rafael de Carvalho Bueno1 · Tobias Bleninger3 · Huaxia Yao2 · James A. Rusak2 Received: 31 January 2020 / Accepted: 7 September 2020 © Springer Nature B.V. 2020
Abstract An internal wave is a propagating disturbance within a stable density-stratified fluid. The internal seiche amplitude is often estimated through theories that describe the amplitude growth based on the Bulk Richardson number (Ri). However, most theoretical formulations neglect secondary effects that may influence the evolution of internal seiches. Since these waves have been pointed out as the most important process of vertical mixing, influencing the biogeochemical fluxes in stratified basins, the wrong estimation may have several impacts on the prediction of the system dynamics. This research paid particular attention to the importance of secondary effects that may play a major role on the basin-scale internal wave amplitude, especially related to the interaction between internal waves and lake boundaries, internal wave depth, and mixing processes due to turbulence. Based on a set of methods, which include auto- and cross-correlations, spectral analysis, and mathematical models, we analyzed the effect of total water depth, wind-resonance, and higher vertical modes on the amplitude growth. We based our analysis on underwater temperature measurements and meteorological data obtained from two small thermally-stratified basins, complemented with numerical simulations. We introduce here a new parametrization which takes into account the total water depth (H), lake length (L), epilimnion thickness ( he ), as well as the resonance effect. We observed that the rate of amplitude growth decreases compared to linear theory when Ri he ∕L ≤ 1 . In these cases, we suggests that previous theories overestimate the internal seiche amplitude, neglecting the instabilities generated near the wave crest due to weak stability and wave interactions. However, under shallow thermocline conditions, due to extra pressure in the upper layer, the vertical displacement may be higher than that predicted by the linear theory. Keywords Basin-scale internal wave · Lake classification · Internal wave parametrization · Lake modeling.
* Rafael de Carvalho Bueno [email protected]; [email protected] 1
Graduate Program on Environmental Engineering, Federal University of Paraná, Curitiba, Brazil
2
Dorset Environmental Science Centre, Dorset, ON, Canada
3
Department of Environmental Engineering, Federal University of Paraná, Curitiba, Brazil
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Vol.:(0123456789)
Environmental Fluid Mechanics
1 Introduction Internal gravity waves are a propagating disturbance within a stable density-stratified fluid, and have been observed to have great impact on many stratified ecosystems, such as atmosphere [50], ocean [56], lakes, and reservoirs [23]. In closed stratified systems, generally called basins, such as lakes and reservoirs, the most common type of waves is the basinscale inte
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