Now, the area under the spectrum represents the total energy that has been transformed to the wind. So, the energy is constant now see the entire energy might have gone to produce waves only in direction 1. But you can also assume that, look this entire energy spread some part of it is actually producing waves in direction 1 and another part is in direction 2 etcetera.
So, integration of this which represents energy always must remain constant, so this must be equal to this, but then this is I have done where also represents the energy, same as the 2 D spectrum. So, this integration must be equal to 1, see then this condition gets satisfied this is the basic philosophy actually, what I am trying to say I will I will give an example numerically will be easier; say let us say this energy is equal to 100 unit, now this the total energy is 100 unit of waves.
Now, the area under the spectrum represents the total energy that has been transformed to the wind. So, the energy is constant now see the entire energy might have gone to produce waves only in direction 1. But you can also assume that, look this entire energy spread some part of it is actually producing waves in direction 1 and another part is in direction 2 etcetera.So, integration of this which represents energy always must remain constant, so this must be equal to this, but then this is I have done where also represents the energy, same as the 2 D spectrum. So, this integration must be equal to 1, see then this condition gets satisfied this is the basic philosophy actually, what I am trying to say I will I will give an example numerically will be easier; say let us say this energy is equal to 100 unit, now this the total energy is 100 unit of waves.
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