Hydrodynamic Stability of the boundary layer beneath a Stokes wave
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Giri, Gautham
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Abstract
This study aims to refine the linear stability analysis of the laminar boundary layer beneath a Stokes wave in deep waters, drawing on Fedele’s earlier findings. Fedele’s analysis focused on two-dimensional perturbations and employed a ”momentary” stability criterion. Here, we adopt a comprehensive approach by shifting to a full instability criterion, allowing for a more complete understanding of the stability characteristics of the boundary layer. Using Fourier and Chebyshev collocation methods to solve the Orr-Sommerfeld eigenvalue problem, we examine the stability of the flow across a broader parameter space. Our findings suggest that, while the laminar boundary layer remains stable for the momentary stability criterion against infinitesimal disturbances for all Reynolds numbers, the full instability criterion adopted here indicates that the flow may be linearly unstable. This full approach enables us to capture potentially unstable modes that may not be evident under a momentary instability framework. This work suggests that the recent experimental observations of spontaneous turbulence beneath unforced, non-breaking surface waves may be due to the instability of the boundary layer beneath the ocean waves
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Date
2024-12-13
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Text
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Thesis (Masters Degree)