The energetics of large-scale internal wave degeneration in lakes

Field observations in lakes, where the effects of the Earth's rotation can be neglected, suggest that the basin-scale internal wave field may be decomposed into a standing seiche, a progressive nonlinear surge and a dispersive solitary wave packet. In this study we use laboratory experiments to quantify the temporal energy distribution and flux between these three component internal wave modes. The system is subjected to a single forcing event creating available potential energy at time zero (APE). During the first horizontal mode one basin-scale wave period (T-i), as much as 10% and 20% of the APE may be found in the solitary waves and surge, respectively. The remainder is contained in the horizontal mode one seiche or lost to viscous dissipation. These findings suggest that linear analytical solutions, which consider only basin-scale wave motions, may significantly underestimate the total energy contained in the internal wave field. Furthermore, linear theories prohibit the development of the progressive nonlinear surge, which serves as a vital link between basin-scale and sub-basin-scale motions. The surge receives up to 20% of the APE during a nonlinear steepening phase and, in turn, conveys this energy to the smaller-scale solitary waves as dispersion becomes significant. This temporal energy flux may be quantified in terms of the ratio of the linear and nonlinear terms in the nonlinear non-dispersive wave equation. Through estimation of the viscous energy loss, it was established that all inter-modal energy flux occurred before 2T(i); the modes being independently damped thereafter. The solitary wave energy remained available to propagate to the basin perimeter, where although it is beyond the scope of this study, wave breaking is expected. These results suggest that a periodically forced system with sloping topography, such as a typical lake, may sustain a quasi-steady flux of 20% of APE to the benthic boundary layer at the depth of the metalimnion.