How to measure the difference between two frames given a set of pixel units for each frame?

I am using a dense optical flow algorithm in order to calculate the optical flow on a given video, after I run the algorithm I receive the output bellow.

I would like to find a way to sum up the changes between two frames (or two sets of vectors (in pixel units)), meaning to find a numerical value to the change between frames in order to determine if these two frames are "similar" or "different"

this is the output (from what I understand, for each pixel it is the change x, y basically):

flow
[[[ 0.00080293  0.00456178]
  [ 0.0023454   0.00762859]
  [ 0.00337119  0.01088941]
  ...
  [ 0.08646814  0.17195833]
  [ 0.07680464  0.15070145]
  [ 0.04990056  0.09711792]]

 [[ 0.00197109  0.00610898]
  [ 0.00431191  0.01074001]
  [ 0.00629149  0.01567514]
  ...
  [ 0.11541913  0.23083425]
  [ 0.10006026  0.19827926]
  [ 0.06407876  0.12646647]]

 [[ 0.00333168  0.0071025 ]
  [ 0.00625938  0.01281219]
  [ 0.01047979  0.02093185]
  ...
  [ 0.15598673  0.31461456]
  [ 0.1284331   0.25725985]
  [ 0.08006614  0.16013806]]

 ...

 [[-0.11634359  0.09029744]
  [-0.14934781  0.11287674]
  [-0.24678642  0.17862432]
  ...
  [ 0.00260158  0.00103487]
  [ 0.00391656  0.00041338]
  [ 0.00312206  0.00064316]]

 [[-0.06021533  0.04847184]
  [-0.07352059  0.05851178]
  [-0.12553327  0.09319763]
  ...
  [ 0.00314228 -0.00119414]
  [ 0.00410303 -0.00139949]
  [ 0.00334636 -0.00098234]]

 [[-0.0192373   0.010998  ]
  [-0.02326458  0.01555626]
  [-0.04161371  0.02764582]
  ...
  [ 0.00236979 -0.00039244]
  [ 0.00327405 -0.00078911]
  [ 0.00281549 -0.00057979]]]
flow
[[[-8.4514404e-03 -9.1092577e-03]
  [-8.2096420e-03 -1.6217180e-02]
  [-9.7641135e-03 -2.3235001e-02]
  ...
  [ 8.4836602e-02  9.4629139e-02]
  [ 7.0593305e-02  7.2248474e-02]
  [ 6.2410351e-02  5.8204494e-02]]

 [[-1.6573617e-02 -1.5174728e-02]
  [-1.5833536e-02 -2.2253623e-02]
  [-1.7538801e-02 -3.1138226e-02]
  ...
  [ 1.3201687e-01  1.3085920e-01]
  [ 1.1270510e-01  1.0012541e-01]
  [ 1.0345179e-01  8.3722569e-02]]

 [[-2.1787306e-02 -2.0292744e-02]
  [-2.2391599e-02 -2.8152039e-02]
  [-2.3549989e-02 -3.8980592e-02]
  ...
  [ 1.5739001e-01  1.6933599e-01]
  [ 1.3471533e-01  1.2855931e-01]
  [ 1.2196152e-01  1.0327549e-01]]

 ...

 [[-3.9006339e-03 -3.0767643e-03]
  [-1.8084457e-02 -8.7532159e-03]
  [-4.0460575e-02 -1.6521217e-02]
  ...
  [ 5.4473747e-03 -1.9708525e-03]
  [ 4.3195980e-03 -1.6532388e-03]
  [ 2.4038905e-03 -2.6415614e-04]]

 [[-2.2322503e-03 -3.0169063e-03]
  [-1.1787469e-02 -8.9037549e-03]
  [-2.8192652e-02 -1.6921449e-02]
  ...
  [ 1.9799198e-03 -3.8150212e-04]
  [ 1.5747466e-03 -5.4049061e-04]
  [ 9.2306529e-04 -1.1204407e-04]]

 [[-1.1798806e-03 -1.9108414e-03]
  [-6.6612735e-03 -5.3157108e-03]
  [-1.6056010e-02 -9.3358066e-03]
  ...
  [ 4.8137631e-04  6.4036541e-04]
  [ 3.4130082e-04  3.7227676e-04]
  [ 1.7955518e-04  1.8480681e-04]]]...

this id the code we are using for the optical flow calculation:

def _calc_optical_flow_(distance_array):
    cap = cv2.VideoCapture("videos/3.1.avi")
    output_file_text = open("output.txt", "w+")

    ret, frame1 = cap.read()
    prvs = cv2.cvtColor(frame1, cv2.COLOR_BGR2GRAY)
    hsv = np.zeros_like(frame1)
    frames_array.append(frame1)

    hsv[..., 1] = 255
    count = 0
    distance = 0


    while(1):
        ret, frame2 = cap.read()
        if frame2 is None:
            break
        frames_array.append(frame2)
        next = cv2.cvtColor(frame2,cv2.COLOR_BGR2GRAY)
        flow = cv2.calcOpticalFlowFarneback(prvs, next, None, pyr_scale=0.5, levels=3, winsize=15, iterations=1,
                                            poly_n=5, poly_sigma=1.2, flags=0)
        mag, ang = cv2.cartToPolar(flow[..., 0], flow[..., 1])

        hsv[..., 0] = ang*180/np.pi/2
        hsv[..., 2] = cv2.normalize(mag, None, 0, 255, cv2.NORM_MINMAX)
        rgb = cv2.cvtColor(hsv, cv2.COLOR_HSV2BGR)
        if count == 10:
            count = 0

            output_file_text.write("flow\n")
            output_file_text.write(np.array_str(flow) + "\n")
            distance = function(flow, distance)
            distance_array.append(distance)
            #print ("flow",flow)

        cv2.imshow('frame2',rgb)
        count=count+1
        k = cv2.waitKey(10) & 0xff
        if k == 27:
            break
        elif k == ord('s'):
            #cv2.imwrite('opticalfb.png', frame2)
            #cv2.imwrite('opticalhsv.png', rgb)
            prvs = next

    output_file_text.close()
    cap.release()
    cv2.destroyAllWindows()
    return distance_array