Can anyone explain these wavy lines forming a across in the photo?
I used a Nikon
AF-S DX 18-140mm 3.5-5.6G ED VR at 140mm, ISO was set to 160.
Here is a 1:1 pixel crop:
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It appears to be diffraction from sunlight passing through the leaves in the tree. It's the same thing you'd get intentionally from using a cross screen filter. Had the focus been on the leaves, I expect that the classic "star" pattern would be more obvious.
It strongly appears you were shooting through a chain-link fence, chicken wire, or something else with a diamond-shaped pattern. Here is where I think the fence or wire would be (apologies for my unsteady hand drawing on a laptop trackpad):
The latest photo you uploaded shows even more distinctly what could plausibly be fence wire in the upper right corner, crossing diagonally across the sky in the background. In this photo, your lens appears to be further away from where the putative fence is (i.e., more chain links in the near field of view). Another poorly hand-drawn demonstration where I think the fence is:
The fencing would cause wavy lines parallel to the wires, that only shows up in the defocused areas of your image. In this thread at dpreview.com, user Tom Axford demonstrates how several narrow strips of paper held in front of the lens creates parallel wavy lines:
Now, the reason I think your entire background doesn't have wavy lines is because the purported fencing is a bit further from the front of your lens than the paper strips Tom Axford used to demonstrate the effect. Thus, the background region immediately surrounding each of the wires in the fence would demonstrate diffraction (the cause of the parallel wavy lines).
Agree with scottbb's assessment, you are likely shooting through an obstruction with a diamond pattern, such as a chain-link fence or a net. (Consider this a supplement to scottbb's answer.)
Examination of bokeh balls within the image show "shadows" of the obstruction.
Here is an independent replication of scottbb's overlays. Rather than draw in where I think the fence may be, I highlight only portions of the image where I can see "wavy lines" or a clear difference in clarity from the surrounding area (haziness). I did this while zoomed in extremely closely, so I could not see whether a diamond pattern was being formed until after zooming out at completion.
Here are some pictures of a chain-link fence for comparison. Notice the tone of the haziness reflects the color of the fence:
Strongly doubt any of the following:
"... diffraction from sunlight passing through the leaves in the tree." Such diffraction is unlikely to create such a regular diamond-shaped pattern. "Wavy lines" are also present where there is no sunlight passing through leaves.
Glare, which can create linear streaks of haziness with flare spots that correspond with the lens' glass elements. Glare is unlikely to create a criss-cross, and flare spots are absent in the images.
Obstruction by reeds of grass. While reeds of grass would produce a criss-cross pattern, it wouldn't be so regularly spaced. The haziness would also be expected to have a brownish or greenish tone from color of the reeds.
"Smearing" after cleaning the lens with a dirty cloth. In a diamond pattern?
Heat waves. In a diamond pattern?
A diamond pattern drawn on a filter or the front element of the lens. This possibility can be distinguished from another obstruction by examining multiple uncropped images from different perspectives. A drawing on the lens would not change position relative to the rest of the scene.