I am reading an application note and find a current source circuit as the following. Why the lower AD8610 is needed since the output voltage of the upper AD8610 is determined by VIN and the two 2kΩ resistors?
I don't think the circuit is "funny" at all. Over the years it and its variations have appeared in app notes from many manufacturers.
Because the non-inverting input of the upper opamp is grounded, the entire function of the circuit is to keep the inverting input at 0 V. The circuit is similar to the "classic" constant current circuit that has only one opamp. The lower opamp circuit has some gain, but other than that the constant-current math is the same.
The circuit works to maintain a constant voltage across a constant resistance, thus creating a constant current through anything that is in series with that resistance. While there is a circuit element named "LOAD", see things from the opamp's point of view. Voltage-mode feedback is picked off at the top of the 1 ohm resistor, making that resistor the actual load. As with any normal, linear, inverting opamp circuit, the opamp works to produce a voltage across the load that is the opposite of its input voltage, modified by the feedback network. In this circuit, the feedback network has non-inverting voltage gain, so the output current is 1/11th of the input current.