"crouching down" is correct and usable in written English.
You can use it to describe someone in a physical position - for example: "The tiger was crouching down in the tall grass, waiting to pounce."
Why was she crouching down?
I don't want to go back to crouching down.
Crouching down beside the car, I took a hit.
A photographer was with her, crouching down, testing angles.
"Guess what?" Marie was crouching down to their height when they tumbled breathless into the apartment.
Try crouching down or even standing on a chair – the difference can be dramatic.
On Pink's "Sober" she was ferocious, crouching down to her knees and shouting the song.
My self-esteem was crushed, back then, crouching down at the bottom of society.
Crouching down so he could touch her knees, he asked if she knew how she had been infected.
Fielder protested the out, crouching down before popping up again and crossing his arms over his chest.
On the walls one graffiti artist had painted Bolt crouching down in a starting position looking intently Christ the Redeemer.
