Internal solitary waves (ISWs) of depression are commonly found in the coastal environment and are believed to re-suspend sediments in coastal regions where the waves break. In this research, the direct numerical simulation is used to study the scalar transport induced by the ISWs of depression propagating over a slope-shelf topography. The scalar in this paper is considered to represent the concentrations of very fine suspended solids or pollutants. Vortices are observed from the numerical results at the bottom boundary layer on the slope during the ISW shoaling process, resulting in a scalar transport. All incident ISWs of depression are observed to produce a waveform inversion on the shelf. The scalar transport from a slope to a shelf is the consequence of the combined vortices at the bottom boundary layer and the overturning of the ISWs of depression, and the latter was commonly ignored in previous studies. This study shows that the ISW-induced scalar transport consists of the following four stages: the slip transport, the wash transport, the vortex transport, and the secondary transport. A dimensionless time scales of the four stages are calculated, and the beginning times of the wash transport and the secondary transport are found to be uncorrelated with the slope gradients, taking values of 1.26, 4, respectively.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Perry M. J., Sackmann B. S., Eriksen C. C. et al. Seaglider observations of blooms and subsurface chlorophyll maxima off the Washington coast [J]. Limnology and Oceanography, 2008, 53(5 Part 2): 2169–2179.
Woodson C. B. The fate and impact of internal waves in nearshore ecosystems [J]. Annual Review of Marine Science, 2018, 10: 421–441.
Jackson J. F. E., Elliott A. J. Internal waves in the Clyde Sea [J]. Estuarine, Coastal and Shelf Science, 2002, 54(1): 51–64.
Alpers W., Huang W. On the discrimination of radar signatures of atmospheric gravity waves and oceanic internal waves on synthetic aperture radar images of the sea surface [J]. IEEE Transactions on Geoscience and Remote Sensing, 2011, 49(3): 1114–1126.
Susanto R., Mitnik L., Zheng Q. Ocean internal waves observes [J]. Oceanography, 2005, 18(4): 80.
Vlasenko V., Hutter K. Numerical experiments on the breaking of solitary internal wavesover a slope shelf topography [J]. Journal of Physical Oceanography, 2002, 32(6): 1779–1793.
Boegman L., Ivey G. N., Imberger J. The degeneration of internal waves in lakes with sloping topography [J]. Limnol Oceanogr, 2005, 50(5): 1620–1637.
Cheng M. H., Hsu R. C., Chen C. Y. Laboratory experiments on waveform inversion of an internal solitary wave over a slope-shelf [J]. Environmental Fluid Mechanics, 2011, 11(4): 353–384.
Butman B., Alexander P. S., Scotti A. et al. Large internal waves in Massachusetts Bay transport sediments offshore [J]. Continental Shelf Research, 2006, 26(17-18): 2029–2049.
Stastna M., Lamb K. G. Sediment resuspension mechanisms associated with internal waves in coastal waters [J]. Journal of Geophysical Research, 2008, 113: 193–199.
Puig P., Palanques A., Guillén J. Near-bottom suspended sediment variability caused by storms and near-inertial internal waves on the Ebro mid continental shelf (NW Mediterranean) [J]. Marine Geology, 2001, 178(1–4): 81–93.
Quaresma L. S., Vitorino J., Oliveira A. Evidence of sediment resuspension by nonlinear internal waves on the western Portuguese mid-shelf [J]. Marine Geology, 2007, 246(2): 123–143.
Boegman L., Ivey G. N. Flow separation and resuspension beneath shoaling nonlinear internal waves [J]. Journal of Geophysical Research Oceans, 2009, 114(C2): 309–321.
Aghsaee P., Boegman L., Diamessis P. J. Boundary-layer-separation-driven vortex shedding beneath internal solitary waves of depression [J]. Journal of Fluid Mechanics, 2012, 690: 321–344.
Zhu H., Wang L. L., Tang H. W. Large-eddy simulation of suspended sediment transport in turbulent channel flow [J]. Journal of Hydrodynamics, 2013, 25(1): 48–55.
Grimshaw R., Pelinovsky E., Talipova T. et al. Internal solitary waves: Propagation, deformation and disintegration [J]. Nonlinear Processes in Geophysics, 2010, 17(6): 633–649.
Zhang H. S., Jia H. Q., Gu J. B. Numerical simulation of the internal wave propagation in continuously density-stratified ocean [J]. Journal of Hydrodynamics, 2014, 26(5): 770–779.
Thorpe S. A. Models of energy loss from internal waves breaking in the ocean [J]. Journal of Fluid Mechanics, 2018, 836: 72–116.
Sakai T., Redekopp L. G. A parametric study of the generation and degeneration of wind-forced long internal waves in narrow lakes [J]. Journal of Fluid Mechanics, 2010, 645: 315–344.
Fang X. H., Jiang M. S., Du T. Dispersion relation of internal waves in the western equatorial Pacific Ocean [J]. Acta Oceanologica Sinica, 2000, (4): 37–45.
Ostrovsky L. A. Evolution equations for strongly nonlinear internal waves [J]. Physics of Fluids, 2003, 15(15): 2934–2948.
Zhu H., Wang L. L., Tang H. W. Large-eddy simulation of the generation and propagation of internal solitary waves [J]. Science China Physics Mechanics and Astronomy, 2014, 57(6): 1128–1136.
Thompson D. A., Karunarathna H., Reeve D. Comparison between wave generation methods for numerical simulation of bimodal seas [J]. Water Science and Engineering, 2016, 9(1): 3–13.
Aghsaee P., Boegman L., Lamb K. G. Breaking of shoaling internal solitary waves [J]. Journal of Fluid Mechanics, 2010, 659: 289–317.
Masunaga E., Homma H., Yamazaki H. Mixing and sediment resuspension associated with internal bores in a shallow bay [J]. Continental Shelf Research, 2015, 110(8): 807–807.
Wang W., Huai W. X., Gao M. Numerical investigation of flow through vegetated multi-stage compound channel [J]. Journal of Hydrodynamics, 2014, 26(3): 467–473.
This work was supported by the Special Fund of State Key Laboratory of China (Grant No. 20185044412), the 111 Project (Grant No. B17015).
Project supported by the National Key Research and Development Program of China (2016YFC0401703, 2017YFC0405605) and the National Natural Science Foundation of China (Grant Nos. 51879086, 51609068, 51709126)
Biography: Jin Xu (1992-), Male, Ph. D.
About this article
Cite this article
Xu, J., Wang, L., Tang, H. et al. Scalar transport by propagation of an internal solitary wave over a slope-shelf. J Hydrodyn 31, 317–325 (2019). https://doi.org/10.1007/s42241-018-0159-6
- Internal solitary waves
- scalar transport
- wave inversion
- dimensionless time scale