Help understanding the voltage waveforms across the components of a series RL circuit
ESR of an inductor is a linear circuit element and would not produce such behavior.  What you have there is some severe non-linearity caused by some unknown element in your circuit.

E.g. the power supply that generates the 1 kHz voltage waveform could be drooping the voltage because it runs into current/power saturation.  Perhaps there are some non-linear circuit elements that you did not draw but which are present in the actual circuit.

Try plotting the output voltage waveform.  My suspicion is that you won't see a perfect 1 kHz sine wave.  This would be especially true if you are using a signal generator to produce the signal.  Signal generators are known to have very large output impedance.