Edge waves generated by atmospheric pressure disturbances moving along a shoreline on a sloping beach

• We investigate edge waves by moving atmospheric disturbances parallel to the shoreline.
• Contour and numerical integrations are used to obtain the solution.
• Edge waves propagate along the shoreline in a packet form of time-varying finite extent.
• Surface elevation is affected by both the bottom slope and atmospheric properties.

Edge waves generated by moving atmospheric disturbances parallel to the shoreline are investigated. Following a standard transformation method, an analytical expression of the surface elevation is derived, which consists of an infinite number of modes. Each mode is expressed as the sum of three singular integrals. Using the contour integration method, these singular integrals are converted to regular integrals, which are evaluated by numerical integration methods. The numerical results of two atmospheric pressure distributions studied by Greenspan (1956) are presented, and the resonance conditions are discussed.