Intrinsic breaking of internal solitary waves in a Deep Lake

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Abstract

Based on simulations with the Dubreil-Jacotin-Long (DJL) equation, the limiting amplitude and the breaking mechanisms of internal solitary waves of depression (ISWs) are predicted for different background stratifications. These theoretical predictions are compared to the amplitude and the stability of the leading internal solitary waves of more than 200 trains of ISWs observed in the centre of a sub-basin of Lake Constance. The comparison of the model results with the field observations indicates that the simulated limiting amplitude of the ISWs provides an excellent prediction of the critical wave height above which ISWs break in the field. Shear instabilities and convective instabilities are each responsible for about half of the predicted wave breaking events. The data suggest the presence of core-like structures within the convectively unstable waves, but fully developed and stable cores were not observed. The lack of stable trapped cores in the field can be explained by the results from dynamic simulations of ISWs with trapped cores which demonstrate that even slight disturbances of the background stratification cause trapped cores to become unstable. © 2012 Preusse et al.

Figures

  • Figure 1. Experimental design. A) Bathymetry of Lake Constance and the location of the main study site (square), B) Zoom into Lake Überlingen with deployment stations from October 2010 (A–D), main study site B (square) and thalweg (broken line). The shaded area depicts depths $100 m. doi:10.1371/journal.pone.0041674.g001
  • Figure 2. Simulation of a measured ISW. Fields of (A) temperature, (B) along-shore velocity (missing values are white) and (C) vertical velocity of a solitary-like wave as observed at station D (colours) and as simulated by the DJL equation (black thick lines). doi:10.1371/journal.pone.0041674.g002
  • Figure 3. Correlation between the occurrence of ISWs with density inversions and ISWs with amplitudes exceeding their simulated amplitude limits Alim. (A) Scatter plot separating shear (red and circles) and breaking (blue and squares) limited ISWs and showing the correlation between Alim and Aobs. The limit, above which breaking is expected, is indicated by the broken line. ISWs with density inversions are depicted as circles and squares, violently breaking waves are intensively coloured. ISWa – ISWd are shown in Fig. 5. (B) Probability to observe waves within ranges of Aobs/Alim (red line, denoted as probability density, values for shaded areas are depicted) and probability to observe waves accompanied by density inversions (blue lines, denoted as proportion) within ranges of Aobs/Alim. doi:10.1371/journal.pone.0041674.g003
  • Figure 4. Measured breaking limited waves. Measured examples of (A) waves with trapped cores during autumn with a filled area between the contour-lines at 15.5uC and 15.75uC, (B) a wave with a perturbed trapped core during spring with a filled area between the contour-lines at 9.5uC and 9.75uC, (C) small waves with trapped cores during spring with a filled area between the contour-lines at 15uC and 15.25uC and (D) breaking limited waves without significant inversions during summer. The temperature difference spanned by the 2 m -inversion in the second wave is 0.014uC, slightly above the accuracy range of 0.01uC. doi:10.1371/journal.pone.0041674.g004
  • Figure 5. Increase and decrease of ISW amplitude with propagation distance of a shear limited wave observed on 26 October 2010. The grey area denotes simulated (Aobs/Alim .1), the black square indicates observed (density inversions) wave breaking. doi:10.1371/journal.pone.0041674.g005
  • Figure 6. Ratio of the number of waves with amplitudes bounded by the breaking limit and waves with amplitudes bounded by shear limit depicted for different seasons (spring: April, May, summer: June – August, autumn: September, October). Black bars correspond to all waves, grey bars to waves simulated to break (Aobs/Alim $1). doi:10.1371/journal.pone.0041674.g006
  • Figure 7. A simulated breaking limited wave encountering a perturbation. Dynamical simulations of (A) a wave with a quasi-steady core and (B–D) a perturbation of the wave in (A), 20, 40 and 60 min after a disturbance (a patch of light (black) fluid in the top 2.4 meters of the water column) was introduced upstream of the wave. Isotherms are given in 0.25uC intervals. doi:10.1371/journal.pone.0041674.g007

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APA

Preusse, M., Stastna, M., Freistühler, H., & Peeters, F. (2012). Intrinsic breaking of internal solitary waves in a Deep Lake. PLoS ONE, 7(7). https://doi.org/10.1371/journal.pone.0041674

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