like a cat chasing its tail 徒劳无功的追求
chase /tʃeɪs/
v.追逐；追赶；追求；追捕；催促；镂刻；求爱；急奔；努力获得；争取得到
n.追逐；追赶；追捕；争取；打猎；努力获得
like a cat chasing its tail：“像猫追自己的尾巴”。不管是猫还是狗，有时候它们会追着自己尾巴转圈圈，但是最后一无所获。所以这个短语被用来比喻“徒劳无功的追求”。例如：
People and happiness is just like a cat with its tail, when the cat is desperately chasing its tail, tail always run faster than it, when the cat decided to always forward tail will closely follow it.
人与幸福就像一只带着尾巴的猫，当猫拼命地追赶它的尾巴时，尾巴总是跑得比它快，当猫决定永远向前时尾巴就会紧紧地跟着它。《王子与贫儿》
What he dreams about is like a cat chasing its tail.
他所追求的都是徒劳的。
也可以说：
chase your (own) tail
瞎忙活；徒劳无功
You're chasing your tail here.
你在这里徒劳无功。
下面是一些花式“徒劳无功，徒劳”的表达法：
His efforts were to no avail.
他徒劳无功。
The doctors tried everything to keep him alive but to no avail.
医生千方百计想使他活下来，但无济于事。
I apologized repeatedly, but to little avail.
我一再道歉，但丝毫没有奏效。
He had the duty receptionist almost jumping through hoops for him. But to no avail.
值班的接待员几乎为他费尽了力气，但还是没用。
receptionist /rɪˈsepʃənɪst/ n.接待员
jump through hoops（为取悦他人或达到目的而）经受苦难，作出很大努力
to no avail徒劳无功
Efforts to reach the people named in the report proved unavailing
联系过报告中所提到的那些人，但都徒劳无功。
He died after a brave but unavailing fight against a terminal illness.
在与绝症进行了一番勇敢但却徒劳的抗争之后，他还是去世了。
terminal /ˈtɜːrmɪnl/
n.终点站；（电路的）端子，线接头；终端机；终端；航空站；航空终点站
adj.末端的；晚期的；致命的；患绝症的；不可救药的；不治的；无可挽回的
The crew fought a losing battle to try to restart the engines.
全体船员努力尝试重新启动发动机，但结果徒劳无功。
The British establishment seems to be off on another quest for fool's gold.
这家英国机构似乎开始了又一次徒劳无功的探索。
quest /kwest/
n.追求(幸福等)；探索；寻找
vi.探索；探求
fool's gold 注定失败的计划；虚幻的摇钱树;愚人金(指黄铁矿)
I wanted to sort out this problem with him, but it was like banging my head against a brick wall.
我曾想跟他把这个问题给解决了，但结果徒劳无功。
She got nothing but trouble for her efforts. 她的努力不但徒劳无功，反而惹来一身麻烦。
As an inexperienced teacher, I tried every means to get them to be quiet, but in vain.
作为一个没有经验的老师,我想尽一切办法让他们安静下来,但徒劳无功。
He shouted after them, vainly trying to attract their attention.
他在他们的后面高喊，想引起他们的注意，却是徒劳。
It would be idle to pretend the system is perfect.
假装系统完美无疵是徒劳的。
idle /ˈaɪdl/
adj.空闲的；闲置的；懒惰的；闲散的；懈怠的；没有工作的；漫无目的的
v.空转；无所事事；(尤指暂时地)关闭工厂，使(工人)闲着；挂空挡；闲荡；未熄火；混时间
It is idle to pretend that their marriage is a success.
佯称他们的婚姻有多美满是无意义的。
After a fruitless morning sitting at his desk he had given up.
他在书桌前徒劳地坐了一上午之后便放弃了。
Our efforts to persuade her proved fruitless.
我们努力说服她，但毫无成效。
Four years of negotiation ended fruitlessly last December.
历时4 年的谈判在去年 12 月无果而终。
negotiation /nɪˌɡoʊʃiˈeɪʃn/
n.谈判；协商；磋商
We have had meaningful negotiations and I believe we are very close to a deal.
我们已进行了有益的磋商，我相信我们很快能成交。
It was a vain attempt to shift the responsibility for the murder to somebody else
试图将谋杀的罪责转嫁给他人是徒劳的。
He underwent a knee operation in the vain hope of getting into the team.
他做了膝盖手术，徒劳地指望能进入该队。
The criminals vainly sought concealment from the searchlight.
罪犯们徒劳地躲闪着探照灯光。
seek /siːk/
v.寻找；寻求；寻求（或追求）…的；试图；谋求；争取；(向人)请求
第三人称单数：seeks现在进行时：seeking 过去式：sought 过去分词：sought
concealment /kənˈsiːlmənt/
n.隐藏；隐瞒；掩盖
Parents campaigned in vain for her reinstatement.
父母们呼吁给她复职，但结果却只是徒劳。
reinstatement /ˌriːɪnˈsteɪtmənt/ n.(法律、服务、做法等的)恢复；复职;复位
The leader of the Liberal Democrats accused the Prime Minister of whistling in the wind to raise Conservative party morale.
自由民主党领导人指责首相鼓舞保守党士气之举根本就是徒劳。
whistle in the wind白费口舌， 徒然无功
类似：
cast stones against the wind
beat the wind
He tried to varnish over the facts, but it was useless.
他想粉饰事实，但那是徒劳的。
varnish /ˈvɑːnɪʃ/ n.清漆；指甲油；罩光漆
vt.给…涂清漆；上清漆；涂指甲油
It is always futile to try to hold back the progress of history.
要想阻止历史潮流是徒劳的。
futile /ˈfjuːtl/ /ˈfjuːtaɪl/
adj.徒劳的；无效的；徒然的
