Complex sentence: Not all solutions of the gradient wind speed yield physically plausible results: the right-hand side as a whole needs be positive because of the definition of speed; and the quantity under square root needs to be non negative.
Split into simpler sentences: Not all solutions of the gradient wind speed yield physically plausible results. The summed-up right-hand side needs be positive because of the definition of speed, and the quantity under square root needs to be non negative.