Yuan, C; Grimshaw, R; Johnson, E; (2018) The Evolution of Internal Undular Bores over a Slope in the Presence of Rotation. Studies in Applied Mathematics , 140 (4) pp. 465-482. 10.1111/sapm.12207.

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Abstract

The large‐amplitude internal waves commonly observed in the coastal ocean often take the form of unsteady undular bores. Hence, here, we examine the long‐time combined effect of variable topography and background rotation on the propagation of internal undular bores, using the framework of a variable‐coefficient Ostrovsky equation. Because the leading waves in an internal undular bore are close to solitary waves, we first examine the evolution of a single solitary wave. Then, we consider an internal undular bore, for which two methods of generation are used. One method is the matured undular bore developed from an initial shock box in the Korteweg–de Vries equation, that is the Ostrovsky equation with the rotational term omitted, and the other method is a modulated cnoidal wave solution of the same Korteweg–de Vries equation. It transpires that in the long‐time model simulations, the rotational effect disintegrates the nonlinear waves into inertia‐gravity waves, and then there emerge complicated interactions between these inertia‐gravity waves and the modulated periodic waves of the undular bore, especially at the rear part of the undular bore. However, near the front of the undular bore, nonlinear effects further modulate these waves, with the eventual emergence of nonlinear envelope wave packets.

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