Two New, Comprehensive Models of Dissipation Rates for Capillary-Gravity Waves, with an Emphasis on Ocean Swell
Open Access
- Author:
- Rajan, Girish Kumar
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- December 01, 2014
- Committee Members:
- Diane Marie Henderson, Dissertation Advisor/Co-Advisor
John Michael Cimbala, Committee Chair/Co-Chair
Diane Marie Henderson, Committee Chair/Co-Chair
James Joseph Brannick, Committee Member
Savas Yavuzkurt, Committee Member
Laura Pauley, Committee Member
Karen Ann Thole, Committee Member
Harvey Segur, Special Member - Keywords:
- Dissipation/Decay
Capillary-Gravity
Surfactant
Marangoni/Elastic Waves
Resonance
Barotropic/Baroclinic Modes
Ocean Swell - Abstract:
- Linear dissipation rates of capillary-gravity waves in both laboratory and ocean settings are investigated in this dissertation. Two new models are formulated to include the effects of an upper fluid and interfacial conditions. The first is a two-fluid surfactant model in which the surfactant-adsorbed interface is treated as a contaminated monolayer. The second is a three-fluid model in which two semi-infinite fluids are separated by a thin layer of Newtonian fluid such that there are two distinct interfaces, which are treated as contaminated monolayers. In principle, the three-fluid model is the most general of all models available in literature. In the three-fluid model, dissipation rates are derived for wave propagation in both the barotropic mode, in which the displacements of the two interfaces are in phase with each other; and the baroclinic mode, in which the interfacial displacements are out of phase. Within the framework of the two-fluid surfactant model, a dispersion relation is derived for the elastic waves at the contaminated interface, and used in a mathematical analysis to show that the dissipation rates of the gravity waves are maximized when the gravity waves are in resonance with the elastic waves. Numerical parametric studies are conducted to analyze gravity waves in an air-oil-water system using the barotropic three-fluid model. The results of the parametric studies are used to classify the gravity waves in the system into three frequency regimes based on the mechanism that dominates the energy transfer. For waves of frequencies less than about 0.1 Hz, the dominant mechanism is the loss of energy to air. For waves of intermediate frequencies about 1 Hz, the dominant mechanism is the loss of energy to the thin layer of oil separating the air and water. For waves of higher frequencies (about 3 Hz) near the limit of gravity waves, the dominant mechanism is the loss of energy to the elastic waves at the contaminated interfaces. The barotropic three-fluid model is also investigated experimentally for standing water waves of frequencies 1 Hz, 1.6 Hz, and 2 Hz, where varying amounts of oil are deposited on the water surface. The emphasis in this dissertation is to understand dissipation of ocean swell; however, the models have been developed for general fluid systems and may thus be used to obtain the dissipation rates of capillary-gravity waves propagating in a system comprising fluids of arbitrary densities and viscosities.