AIMS Seminar | Ali Aghayev (McMaster University)

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 derivation of travelling wave reductions where steady solutions with constant speed c lead to the Babenko formulation.
  • The construction of small-amplitude (Stokes) expansions for the wave profile ? and the dispersion relation c².
  • A comparison between expansions in conformal depth versus physical depth, identifying specific discrepancies in existing literature regarding high-order asymptotic analysis.