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How does this make sense? Energy density is usually a function of position (maybe time,frequency also) How could it also be a function of $\Omega$ , i.e the solid angle ?
For context, $ u(\Omega)$ appears in the theory of radiative energy transfer...
Here is one example. Consider neutrons in motion, preferentially in a direction $\vec \Omega$ about a particular point, and the neutrons interact with the nuclei in the surrounding medium in a nuclear reaction that releases energy, fission for example. The energy density is greatest in the direction where the neutrons preferentially move. This is modeled using the Boltzmann transport equation (an integro-differential equation) considering the angular neutron flux. See a textbook on nuclear reactor theory, such as Nuclear Reactor Theory by Bell and Glasstone.
