Open Collections

Wang, Xuemeng

University of British Columbia

This thesis explores the damping and cessation of surface waves in an inviscid layer, particularly under the influence of a floating, dissipative plate. Experimental results [39, 40, 70] indicate that when a floating particle layer is present, surface waves will come to rest in a finite time. In particular, the cessation process experiences a transition from exponential decay to finite-time decay in a power-law manner when wave amplitudes are sufficiently small. This pattern potentially resembles a jamming effect [70]. To theoretically elucidate the cessation time of surface waves and the shift in wave attenuation laws, we construct a two-layer model. The model combines inviscid shallow water theory with plate theory under the long-wavelength limit. The top layer is treated as a plate, as we establish that it has constant thickness. For plate theory, this model characterizes the top plate using a range of models. This includes a viscoplastic plate modeled following the Herschel-Bulkley constitutive law. An exploration of the en- ergetics captured by the model suggests that waves decay to rest in a finite time. This result is confirmed using a combination of approximate, numer- ical, and asymptotic solutions to the model equations. In the limit that the plate behaves like a perfectly plastic material, the sloshing motions take the form of triangular waves with bending restricted to narrow viscoplastic hinges. Additionally, alternative models are considered for a more accurate explanation of the decaying pattern observed experimentally [39, 40, 70]. These alternatives include One-Way Bingham (OWB) models, a two-phase model, and Boyer et al.’s model [11]. OWB models address the impact of particle dilation and compaction on Bingham plate bending by modulating the yield stress and viscous force. For the two-phase model, we illustrate that scaling consistency is ensured when the difference between the total plate density and the fluid phase density is small. In addition, Boyer et al.’s model is incorporated into the two-phase scheme for further insights.

Text

2024-04-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/87910

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/