A note on free and forced Rossby wave solutions: the case of a 2 straight coast and a channel

• Main Author: FEDERICO GRAEF ZIEHL
• Format: Article in Journal/Newspaper
• Language: Spanish
• Published: 2017
• Subjects: info:eu-repo/classification/Autor/Planetary waves; Channel flow; Modes; Coast effect; Solutions; info:eu-repo/classification/cti/1; info:eu-repo/classification/cti/25; info:eu-repo/classification/cti/2510; info:eu-repo/classification/cti/251007; Denmark Strait
• Online Access: http://cicese.repositorioinstitucional.mx/jspui/handle/1007/2784

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially “decaying” and exponentially “growing” RW could be excited in the channel.