Mass transport in internal coastal Kelvin waves. (English) Zbl 1297.86007
Summary: We investigate theoretically the mass transport in internal coastal Kelvin waves by integrating the horizontal momentum equations in the vertical. Applying a perturbation method, the time-averaged Lagrangian horizontal fluxes are determined to second order in wave steepness. The linear wave field is expanded in the vertical using orthogonal functions. Due to the orthogonality property of these functions, formulae for the non-linear Stokes drift and the mean vertically-averaged Eulerian transport driven by the radiation stress can be derived for arbitrary vertical variation of the Brunt-Väisälä frequency \(N\). For values of \(N\) typical of the thermocline in the Caspian Sea, the calculation of the non-linear transports yields a jet-like mean flow along the coast, limited in the off-shore direction by the internal Rossby radius. It is suggested that this wave-induced mean drift may contribute to the mean circulation in the Caspian Sea.
MSC:
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
internal coastal Kelvin waves; Lagrangian mass transport; eulerian mean current; Stokes drift; the Caspian seaReferences:
| [1] | Ghaffari, P.; Lahijani, H. A.; Azizpour, J., Snapshot observation of the physical structure and stratification in deep-water of the south Caspian Sea (western part), Ocean Sci., 6, 877-885 (2010) |
| [2] | McCreary, J., Eastern tropical ocean response to changing wind systems: with application to El Niño, J. Phys. Oceanogr., 6, 632-645 (1976) |
| [3] | Busalacchi, A. J.; O’Brien, J. J., The seasonal variability in a model of the tropical Pacific, J. Phys. Oceanogr., 10, 1929-1951 (1980) |
| [4] | Weber, J. E.H.; Broström, G.; Christensen, K. H., Stokes drift in internal equatorial Kelvin waves; continuous stratification versus two-layer models, J. Phys. Oceanogr., 44, 591-599 (2014) |
| [5] | Longuet-Higgins, M. S.; Stewart, R. W., Changes in the form of short gravity waves on long waves and tidal currents, J. Fluid Mech., 8, 565-583 (1960) · Zbl 0094.45301 |
| [6] | Stöylen, E.; Weber, J. E.H., Mass transport induced by internal Kelvin waves beneath shore-fast ice, J. Geophys. Res., 115, C03022 (2010) |
| [7] | Lighthill, M. J., Dynamic response of the Indian Ocean to onset of the southwest monsoon, Phil. Trans. R. Soc. Lond., A265, 45-92 (1969) |
| [8] | Gill, A. E.; Clarke, A. J., Wind-induced upwelling, coastal currents, and sea-level changes, Deep-Sea Res., 21, 325-345 (1974) |
| [9] | Martinsen, E. A.; Weber, J. E.H., Frictional influence on internal Kelvin waves, Tellus, 33, 402-410 (1981) |
| [10] | Stokes, G. G., On the theory of oscillatory waves, Trans. Camb. Phil. Soc., 8, 441-455 (1847) |
| [11] | Longuet-Higgins, M. S., Mass transport in water waves, Phil. Trans. R. Soc. Lond., A245, 535-581 (1953) · Zbl 0050.20304 |
| [12] | Phillips, O. M., The Dynamics of the Upper Ocean (1966), Cambridge University Press: Cambridge University Press New York · Zbl 0193.56902 |
| [13] | Nöst, E., Calculating tidal current profiles from vertically integrated models near the critical latitude in the Barents Sea, J. Geophys. Res., 99, 7885-7901 (1994) |
| [14] | Fjeldstad, J. E., Internal waves of tidal origin, (Part I. Theory and analysis of observations. Part I. Theory and analysis of observations, Geophysica Norwegica, No. 5 (1964)), 1-73, XXV |
| [15] | Williams, R. B.; Gibson, C. H., Direct measurements of turbulence in the Pacific Equatorial Undercurrent, J. Phys. Oceanogr., 4, 104-108 (1974) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
