Let's say that I make an image for an OS that uses a kernel of version 10. What behavior does Docker exhibit if I run a container for that image on a host OS running a kernel of version 9? What about version 11?
Does the backward compatibility of the versions matter? I'm asking out of curiosity because the documentation only talks about "minimum Linux kernel version", etc. This sounds like it doesn't matter what kernel version the host is running beyond that minimum. Is this true? Are there caveats?
Let's say that I make an image for an OS that uses a kernel of version 10.
I think this is a bit of a misconception, unless you are talking about specific software that relies on newer kernel features inside your Docker image, which should be pretty rare. Generally speaking a Docker image is just a custom file/directory structure, assembled in layers via FROM and RUN instructions in one or more Dockerfiles, with a bit of meta data like what ports to open or which file to execute on container start. That's really all there is to it. The basic principle of Docker is very much like a classic chroot jail, only a bit more modern and with some candy on top.
What behavior does Docker exhibit if I run a container for that image on a host OS running a kernel of version 9? What about version 11?
If the kernel can run the Docker daemon it should be able to run any image.
Are there caveats?
As noted above, Docker images that include software which relies on bleeding edge kernel features will not work on kernels that do not have those features, which should be no surprise. Docker will not stop you from running such an image on an older kernel as it simply does not care whats inside an image, nor does it know what kernel was used to create the image.
The only other thing I can think of is compiling software manually with aggressive optimizations for a specific cpu like Intel or Amd. Such images will fail on hosts with a different cpu.