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poilop
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I know that we can find the speed of the wave in shallow water by:
c^2 = gh
but how do we derive it?
c^2 = gh
but how do we derive it?
The shallow water wave equation is a mathematical model that describes the behavior of waves in shallow water, such as the waves seen at the beach or in a lake.
The shallow water wave equation assumes that the water depth is much smaller than the wavelength of the waves, and that the wave amplitudes are relatively small. It also assumes that there is no wind or other external forces acting on the water.
The shallow water wave equation is derived from the Navier-Stokes equations, which describe the motion of fluids. By applying simplifying assumptions and using the principle of conservation of mass and momentum, the shallow water wave equation can be derived.
The shallow water wave equation has various applications in oceanography, coastal engineering, and weather forecasting. It is used to predict the behavior of tsunamis, storm surges, and tides, and to design structures such as breakwaters and harbors.
The shallow water wave equation is only applicable to waves in shallow water, and cannot accurately model waves in deep water. It also does not take into account the effects of wind, currents, and other external forces on the water. Additionally, it assumes a linear relationship between wave height and wavelength, which may not always hold true in real-world scenarios.