I encountered this phrase and after a bit of Googling, it seems to describe the action of crowding around a particular thing or object (people crowding around someone, trees crowding around a building) but doesn't 取り囲む itself also describe that action? Does omitting the 周囲 change the effect of its use in sentences or is it more similar to an idiomatic set phrase?
The sentence i saw it in was:
周囲を取り囲むように大勢の学生が集まっている。
Japanese motion verbs utilize the particle を for both object and place the action takes place. So you can equally say:
彼を取り囲む。
周囲を取り囲む。
彼の周囲を取り囲む。
but not:
× 彼を周囲を取り囲む。 (same case particle cannot be repeated in one clause)
In my opinion, the 周囲を取り囲む version has slightly more "completely surrounded" nuance, but it barely matters in the usual case. Also, the 周囲 can be used as good as a "dummy noun" to bypass obvious pronouns like him, her, it etc. in English. We hate pronouns.
If you'd look for similar expressions in Japanese, they abound:
上を見上げる
後ろを振り返る
下に落ちる
前に進む
︙
Of course, you don't want to translate them literally.
(from http://www.inquisitr.com/6826/for-restrooms-go-back-toward-your-behind/)
Does omitting the 周囲 change the effect of its use in sentences or is it more similar to an idiomatic set phrase?
Yes. Since 取り囲む is a verb, and it is a transitive verb ( you can imagine easily, I think ), so the object is necessary.
Now, onto 周囲
Please take a look at here
http://okjiten.jp/kanji676.html the word 周
Here is how the Kanji 周 was born. You can see the 4 blocks. And you can see also
成り立ち 指事文字です。「方形の箱などの器物 に彫刻が一面に施された」象形から、 「あまねく・ゆきわたる」を意味する 「周」という漢字が成り立ちました。
Translation :
How was the Kanji made?
This is 指示文字 ( I do not know the corresponding English, sorry ( But here http://okjiten.jp/kanji1.html we can learn the 4 patters how Kanji was created ). From the pictograph that looks like a rectangular container or other tools sculptures are decorated outside, the Kanji 周, denoting "all over, far spreading" was made.
the word 囲
http://okjiten.jp/kanji630.html
成り立ち 形声文字です。「周辺を取り囲む線」 の象形（「めぐらす」の意味)と 「ステップの方向が違う足の象形と 場所を示す文字」(「ここでは、 「かこむ」の意味)から、「かこい めぐらす」を意味する「囲」という 漢字が成り立ちました。
Translation
This is 形成文字. From an ideograph denoting "a line surrounding an object" ( enclosure ) and another expression "footage each pointing different directions" the Kanji 囲む denoting "to build a fence" was made.
So, 周囲 is ”far spreading fence ( field ).”
So, when we say ビルの周囲, we mean "the vicinity of the building" due to the derivation from above, like a fence circling the building.
When you say, 周囲を取り囲む, sure, as you say
it seems to describe the action of crowding around a particular thing or object (people crowding around someone,
when people crowd, it becomes a "mass", right? So
ex:（人々の）周囲を取り囲む surrounding people ( of some kind ).
Have a nice Sunday.
