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The KP equation can be used to model water waves of long wavelength with weakly non-linear restoring forces and frequency dispersion. If surface tension is weak compared to gravitational forces , λ = + 1 {\displaystyle \lambda =+1} is used; if surface tension is strong, then λ = − 1 {\displaystyle \lambda =-1} .
Consider a boat moving from right to left with constant speed v, emitting waves of varying wavelength, and thus wavenumber k and phase velocity c(k), of interest when < v for a shock wave (cf., e.g., Sonic boom or Cherenkov radiation). Equivalently, and more intuitively, fix the position of the boat and have the water flow in the opposite ...
Ocean dynamics define and describe the flow of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean. Ocean dynamics has traditionally been investigated by sampling from instruments in situ. [1]
Due to the Coriolis effect, surface water moves at a 90° angle to the wind current. If the wind moves in a direction causing the water to be pulled away from the coast then Ekman suction will occur. [1] On the other hand, if the wind is moving in such a way that surface waters move towards the shoreline then Ekman pumping will take place. [1]
Internal tides are generated as the surface tides move stratified water up and down sloping topography, which produces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other major source of internal waves is the wind which produces internal waves near the inertial frequency.
After the wave breaks, it becomes a wave of translation and erosion of the ocean bottom intensifies. Cnoidal waves are exact periodic solutions to the Korteweg–de Vries equation in shallow water, that is, when the wavelength of the wave is much greater than the depth of the water.
This leads to the formation of a subtropical convergence front. As the water masses on both sides of the front have different temperatures, this creates a strong temperature gradient and makes that such fronts can be seen as thermal fronts. [27] In addition, the build-up of water at this region leads to a slight increase in sea level.
It can be further simplified by realizing that, in basin-scale ocean gyres, the relative vorticity is small, meaning that local changes in vorticity cannot account for the decrease in . [5] Thus, the water parcel must change its planetary vorticity accordingly. The only way to decrease the planetary vorticity is by moving the water parcel ...