A note on free and forced Rossby wave solutions: The case of a straight coast and a channel |
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| Institution: | 1. College of Marine Sciences, Shanghai Ocean University, China;2. Collaborative Innovation Centre for National Distant-water Fisheries, Shanghai Ocean University, China;3. College of Physical and Environmental Oceanography, Ocean University of China, Songling Road 238, Laoshan District, Qingdao 266003, China;4. College of Environmental Science and Engineering, Ocean University of China, China;5. Key Laboratory of Physical Oceanography, Ocean University of China, China;1. American Society of Engineering Education, DC, USA;2. Naval Research Laboratory, Stennis Space Center, MS, USA;3. Florida State University, Tallahassee, FL, USA;4. Vencore, Incorporated, Stennis Space Center, MS, USA;5. Faculty of Science, Hokkaido University, Sapporo, Japan;6. Faculty of Fisheries, Kagoshima University, Kagoshima, Japan;7. Department of Ocean Sciences, Inha University, Incheon, South Korea;1. Centre IRD (Institut de Recherche pour le Développement), Nouméa, New Caledonia;2. Université de Toulouse, UPS (OMP-PCA), LEGOS, 14 Avenue Edouard Belin, F-31400 Toulouse, France;3. IRD, LEGOS, F-31400 Toulouse, France;4. Sorbonne Universités (UPMC, Univ Paris 06)-CNRS-IRD-MNHN, LOCEAN Laboratory, IPSL, Paris, France |
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| Abstract: | 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. |
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| Keywords: | Planetary waves Channel flow Modes Coast effect Solutions |
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