By William Geraint Vaughan Rosser
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J Phys Oceanogr 26:21–37 Huang NE, Shen SS (eds) (2005) Hilbert-Huang transform and its applications. , Singapore, 311 p Huthnance JM (1989) Internal tides and waves near the continental shelf edge. Geophys Astro Fluid 48:81–106 Kahru M (1983) Phytoplankton patchiness generated by long internal waves: a model. Mar EcolProg Ser 10:111–117 Konyaev KV, Sabinin KD, Serebryany A (1995) Large amplitude internal waves at the Mascarene Ridge in the Indian Ocean. Deep-Sea Res 42:2075–2091 Korteweg DJ, de Vries G (1895) On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
If f 2 Thus Eq. 8) From Eq. 9) If waves propagate upwards into a region of√increasing frequency N0 in the N 2 − ω2 and the wavelength thermocline, wavenumber kz increases as 1/2 2 2 λ = 2π/(kx + kz ) is reduced. 10) in which a is the amplitude of internal wave and ρ0 is a reference density. In absence of mean shear and negligible dissipation, the wave amplitude, a, varies −1/2 roughly as N0 , and attenuates as upward propagating waves encounter the thermocline (Thorpe 2005). However, when frequency N0 decreases to values less than ω, wavenumber kz tends to infinity and wave are reflected.
For shallow seas such as the Baltic Sea, the vertical density structure exhibits the three-layer profile when surface and bottom uniform layers are separated by a non-uniform layer. If the density profile in the non-uniform layer is approximated by the exponential function, the boundary value problem for the three-layer density profile was solved analytically in Sect. 3. Some other density profiles are discussed in Sect. 4. For a more complex density profile, an analytical solution is not possible.