Is the flow of current in this RL circuit ambiguously defined?
Before closing the switch:


Initially inductor was an open circuit. At the steady state it can be assumed as a short, and a steady state current \$I  \$ will flow "downwards", through 2 ohms and the inductor. The value of it will be \$ 2* \frac {8}{(2+8)} \$ = 1.6 A. 


After closing the switch:


The inductor will act like a current source and it sources a current \$ I_L\$ = 1.6 A at t = 0 . "Downwards" itself. Because an inductor opposes any change in current through it . An emf is induced, and as per lenz' law, the effect of the induced emf in L will be to keep the current flowing in the same direction.
Equivalent circuit after shorting:




Apply KCL at any node where currents meet. So at any moment t > 0 ,$$i_2 + i_L = 2$$
$$ i_ 2= 2 - i_L$$