AIMS Seminar | Ali Aghayev (McMaster University)
Mar 2, 2026
11:30AM to 12:30PM
Date/Time
Date(s) - 02/03/2026
11:30 am - 12:30 pm
Speaker: Ali Aghayev (McMaster University)
Location: Hamilton Hall, Room 403
Title: Stokes Waves in a Fluid of a Finite Depth
Abstract: This work explores the formulation of free surface Euler equations using conformal variables to derive Babenko’s equation for a fluid of finite depth h0. By considering two-dimensional 2?-periodic waves, we establish the relationship between physical depth and conformal depth through the mean value of the surface elevation ?.
The study utilizes a Lagrangian functional with Lagrange multipliers to preserve constraints and derive the system’s equations of motion. Key highlights include:
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The derivation of travelling wave reductions where steady solutions with constant speed c lead to the Babenko formulation.
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The construction of small-amplitude (Stokes) expansions for the wave profile ? and the dispersion relation c2.
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A comparison between expansions in conformal depth versus physical depth, identifying specific discrepancies in existing literature regarding high-order asymptotic analysis.
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