8.3 The waves discussed in this question are known as internal gravity waves. As

Question

8.3 The waves discussed in this question are known as internal gravity waves. As shown in this example, the frequency of these waves depends on the Brunt–Väisälä frequency and the horizontal and vertical wavenumber of the wave.

(a) For an atmosphere with N = 0023 s1 find the frequency of waves with:

(i) k = 314×(10^3) m1

and m = 458×(10^3) m1;

(ii) k = 628×(10^3) m1

and m = 574×(10^3) m1.

(b) What is the horizontal and vertical wavelength of these waves?

(c) Calculate the horizontal and vertical phase speed of these waves.

(d) Calculate the horizontal and vertical group velocity of these waves.

(e) Are these waves dispersive? Why or why not?

Explanation / Answer

(a)

Frequency of the gravity wave is given by,

(i).

b)

The horizontal wavelength of the wave is given by,

         The vertical wavelength of the wave is given by,

       c) The horizontal phase speed of the waves is,

            The vertical wave speed of the wave is,

   d) Horizontal Group velocity of the waves is,

       Vertical group velocity of the wave is,

e) The above waves are dispersive since they are dependent on frequencies of the waves.

Follow the same procedure to calculate for second set of waves.

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