Solution 1:

It appears there are no specific terms for the ways a cat moves its tail, despite the many and different signals it may send.

The tail says it all: Watching a cat's tail is an excellent way to determine how they are feeling. If you get bitten by a cat, mostly likely you missed the warning signs.

  • Friendly and raised: Usually a cat with a raised tail (sometimes with a slightly bent tip), accompanied by their ears up high, is happy to see you and might approach you in a friendly greeting. You may also see cats approaching each other with raised tails with bent tips... these cats are being friendly!

  • Wagging tail = bad: Unlike a dog, a wagging cat tail does not mean they are happy to see you! You can tell a lot by a cat tail, and when it's moving in a wag, that generally means something or someone is being annoying.

  • Twitching curiosity: While a lashing cat tail usually implies anger, a little bit of twitching does not necessarily mean that.

  • Fluffy fear: When a cat's tail is puffed up and looks bristled, the cat is feeling afraid, threatened and could either be on the defensive or offensive.This is usually accompanied by an arched back.

Probably one of the very few 'cat-specific' verbs is to purr:

  • (esp of cats) to make a low vibrant sound, usually considered as expressing pleasure, etc.

Solution 2:

I would say it holds its tail quivering in a vertical position when it is happy.

Cats can

  • quiver
  • twitch
  • thump
  • wag
  • flick
  • swish
  • fluff

their tails. All of which means something

As mentioned in another post, the position also means something

According to catster.com

A happy cat holds her tail high, and if she greets you at the door with her tail quivering, she's happy to see you.


(source: dogster.com)

Solution 3:

Cat body language is more complex than simply wagging.

Most people might think swishing is the feline equivalent of wagging. But according to Common Cat Behaviors (Best-Cat-Tips.com), swishing its tail from side to side "may indicate real or mock annoyance."

There are several tail signals identified on that web page. Some others are:

  • tail high and straight up means proud and content
  • tail horizontal behind, or slightly drooping means relaxed, confident and alert
  • tail held vertically and twitching or quivering means very happy, pleased to see you
  • tail held upright and hooked over at the tip means a degree of uncertainty
  • tail held upright and bristling means the cat has become defensively aggressive

And because the subject is cats:

Canis Lupus with his cat

Solution 4:

A cat raises its tail (up) when happy or friendly. [In general, because not all cats do that and not every time they are happy.]

A happy cat raises its tail straight up. A cat may still be happy if their tail is up the in air with the tip curled. It just means that they feel a bit unsure.

https://www.smartlivingnetwork.com/cat-breeds/b/8-signs-your-cat-is-happy/

It is even seen in big cats like African lions:

A friendly cat raises its tail to allow this inspection, but often one is more fearful, keeps its tail down, and sidesteps, so the pair ends up circling.

[The Behavior Guide to African Mammals by By Richard Estes]