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Tham khảo tài liệu 'kundu fluid mechanics 2 episode 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4. Surfattt Cjm ih IIÌUVK 199 of a wave is Doppler shiftedby an amountU K due to the mean Sow. Equation 7.20 is easy to understand by considering a situation in which the intrinsic frequency a is zero and the Sow pattern has a periodicity in the X direction of wavelength 2it k. If this sinusoidal pattern is translated in the X direction at speed u then the observed frequency at a fixed point is a 0 Uk. The effects of mean Sow on frequency win not be considered further in this chapter. Consequently the involved frequencies should be interpreted as the intrinsic frequency. 4. Surface Gravity Waves In this section we shall discuss gravity waves at the free surface of a sea of liquid of uniform depth H which may be large or small compared to the wavelength Ằ. We shall assume that the amplitude a of oscillation of the free surface is small in the sense that both a k and a H are much smaller than one. The condition a k 4C 1 implies that the slope of the sea surface is small and the condition a H 4C 1 implies that the instantaneous depth does not differ significantly from the undisturbed depth. These conditions allow us to linearize the problem. The frequency of the waves is assumed large compared to the Coriolis frequency so that the waves are unaffected by the earth s rotation. Here we shall neglect surface tension in water its effect is limited to wavelengths 7 cm as discussed in Section 7. The fluid is assumed to have small viscosity so that viscous effects are confined to boundary layers and do not affect the wave propagation significantly. The motion is assumed to be generated from rest say by wind action or by dropping a stone. According to Kelvin s circulation theorem the resulting motion is irrotational ignoring viscous effects Coriolis forces and stratification density variation . Formulation of the Problem Consider a case where the waves propagate in the A direction only and that the motion is two dimensional in the xz-planc Figure 7.4 . Let the vertical .
