How does ultrasonic horn produce a convection current in the water? When I was using ultrasonic horn in a beaker, I notice that there are convection currents in the beaker and stir up my substance. I don't understand why it produce water current, I thought that it will just vibrate like the ultrasonic bath. So why does ultrasonic horn create water currents? Thank you.
 A: The word "horn" conveys directionality, i.e. a specific direction in which the energy is transferred. It would be amazing if there were no currents in the liquid considering also reflections from the beaker wall.
In this paper the momentum of a sound wave is calculated. 
Looking up ultrasonic baths  I found this video which shows that there too the momentum is conserved , at 2min 13', except the area where the sound waves are imposed, the bottom of the bath, is large and moving uniformly and one cannot see the momentum transfer because there is no contrast, thus you cannot see a flow. The horn focuses the energy and creates the contrast in motion.
A: It's impossible to say without seeing your experimental setup, but an obvious explanation is that the ultrasound is heating the water and you're seeing plain old thermal convection currents.
You say you don't get convection currents in an ultrasonic bath, but my recollection of using (admittedly quite powerful) ultrasonic baths is that you get quite vigorous currents. I've never looked into whether the currents are thermally stimulated.
A: It's difficult to tell without seeing the whole thing, but ...
If it is ultra(low)-sound it means that the driver for your horn should be very large - like over 15-inch to produce high volume with small displacement of the driver. Small displacement of the driver is critical for producing (in normal working conditions) vibrations of air - which are wave - and not "wind" - which is not wave. 
Majority of commercial loudspeakers these days use very small diameter speakers for the low-end frequencies. This causes a lot of wind as a side-effect (and poor sound quality) of large displacement, which is used to make up for the contracted area of the diaphragm needed to produce these frequencies.
How about placing a piece of paper in front of your horn and watching how it reacts. If it is blown-off, it means your horn is working in sub-optimal setting and the current you are receiving in the water is not that strange perhaps.
