In my eyes, this tells everything. Two transducer/microphone pairs in a nearly orthogonal array should allow not only to calculate the speed of the wind from these two delayed signals, but also the wind direction. Am I the only one to see that this are elementary vector computations? For a simple example, let's have a signal delay between one transducer/mic array corresponding to 357m/s and between the second corresponding to 340m/s (which is default sound propagation speed). From this, we know that the wind direction is in line with array 1 and it is blowing from the transducer to the mic since the propagation speed is increased by 17m/s which logically corresponds to the wind speed...
Now, as a second example, lets measure 347m/s on axis 1 and 333m/s on axis 2, which corresponds to +7m/s and -7m/s. The resulting wind speed vector length will be SQRT(7^2 + (-7)^2) which is about 10m/s. Dividing the measured values by the vector length gives the relative cosines of the angles which the wind forms with the 2 axes which allows to calculate the direction to 45° vs axis 1 and 135° vs axis 2.