После прогулки в парке у меня появляется ощущение спокойствия.

После requires the genitive case.

The base form is прогулка.
In the genitive singular, it becomes прогулки.

So:

• прогулка = a walk
• после прогулки = after a walk

This is a fixed pattern in Russian:

• после работы = after work
• после урока = after the lesson
• после дождя = after the rain

Because here в парке means in the park, describing location, not direction.

Russian uses:

• в + accusative for motion into something
  
  • идти в парк = to go to the park
• в + prepositional for being in a place
  
  • гулять в парке = to walk in the park

In this sentence, the walk takes place in the park, so Russian uses the prepositional case:

• парк → в парке

This is a very common Russian way of expressing that something arises in someone or comes over someone.

Literally, у меня появляется ощущение is something like:

• at me there appears a feeling
• more naturally: I get / I develop a feeling

Russian often uses у + genitive instead of making the person the grammatical subject.

Compare:

• У меня есть книга = I have a book
• У меня появляется ощущение спокойствия = I get a feeling of calm

So у меня marks the person experiencing the feeling.

Because у requires the genitive case.

The pronoun changes like this:

• я = I
• меня = of me / me in genitive

So:

• у меня = at me / with me / in my experience

This is a fixed pattern you will see all the time:

• у меня есть время = I have time
• у меня болит голова = my head hurts
• у меня появляется надежда = hope appears in me / I begin to feel hope

Because the grammatical subject is ощущение, which is singular.

The core of the sentence is:

• ощущение появляется = the feeling appears

Even though English would usually say I feel calm or I get a sense of calm, Russian structures it differently. The thing that appears is ощущение.

Since ощущение is singular neuter, the verb is singular:

• ощущение появляется

If the subject were plural, the verb would also be plural:

• появляются мысли = thoughts appear

Появляется comes from появляться, meaning to appear, to arise, or to come up.

In this sentence it means that the feeling of calm comes over you or arises after the walk.

So the sense is not just a static I have calm, but rather:

• a sense of calm begins to appear
• I start to feel calm
• a calm feeling comes

Because it is imperfective present, it often suggests something habitual or generally true:

• after a walk in the park, this feeling tends to arise

Because спокойствия is in the genitive case after ощущение.

Russian often uses the genitive after nouns to express of relationships:

• чашка чая = a cup of tea
• чувство радости = a feeling of joy
• ощущение спокойствия = a feeling / sense of calm

So:

• ощущение = sensation, feeling
• спокойствие = calm
• спокойствия = of calm

This is very natural Russian.

Russian often expresses of relationships just by changing the case, without using a separate word.

English says:

• a feeling of calm

Russian says:

• ощущение спокойствия

The genitive ending itself does the job that of does in English.

This is one of the most important functions of the genitive in Russian.

Yes, чувство спокойствия is also possible.

Very roughly:

• ощущение = sensation, sense, impression
• чувство = feeling, emotion, sense

In many contexts they overlap.

Here, ощущение спокойствия sounds a little like an inner sensation or sense of calm.
Чувство спокойствия would sound more like a feeling of calm.

Both are understandable and natural, though ощущение спокойствия has a slightly more reflective or descriptive tone.

Most naturally, it sounds like a general or habitual statement:

• after a walk in the park, I tend to feel calm

That comes from the present tense imperfective появляется, which often describes something repeated, typical, or generally true.

If you wanted to emphasize one specific past occasion, you would normally use a past form, for example:

• После прогулки в парке у меня появилось ощущение спокойствия.
  = After the walk in the park, I felt a sense of calm.

Yes, but the meaning changes.

• появляется = appears / arises; usually or generally happens
• появилось = appeared / arose; happened once in the past

So:

• После прогулки в парке у меня появляется ощущение спокойствия.
  = After a walk in the park, I get a sense of calm.
  (general truth / repeated experience)

• После прогулки в парке у меня появилось ощущение спокойствия.
  = After the walk in the park, I got a sense of calm.
  (one particular event in the past)

Yes. Russian word order is flexible, although different orders can sound more or less natural depending on emphasis.

The original sentence is very natural:

• После прогулки в парке у меня появляется ощущение спокойствия.

You could also say:

• У меня после прогулки в парке появляется ощущение спокойствия.
• Ощущение спокойствия появляется у меня после прогулки в парке.

These all mean basically the same thing, but the focus shifts:

• starting with после прогулки в парке highlights when
• starting with у меня highlights who experiences it
• starting with ощущение спокойствия highlights what appears

For a learner, the original order is a good model.

Because this is a normal adverbial phrase at the beginning of the sentence, and in Russian such phrases usually do not need a comma.

So this is standard:

• После прогулки в парке у меня появляется ощущение спокойствия.

A comma would usually appear only if there were some special intonation, parenthetical structure, or another reason for punctuation. In an ordinary sentence like this, no comma is needed.

You can, but the sentence becomes less personal and slightly less clear about who experiences the feeling.

Compare:

• После прогулки в парке у меня появляется ощущение спокойствия.
  = After a walk in the park, I get a sense of calm.

• После прогулки в парке появляется ощущение спокойствия.
  = After a walk in the park, a sense of calm appears.

The second version sounds more general or impersonal, almost like a statement about what happens in such situations. If you want to say I experience it, у меня is helpful and natural.

Yes, but it is not exactly the same in tone.

• Я чувствую спокойствие = I feel calm / I feel tranquility
• У меня появляется ощущение спокойствия = a sense of calm comes over me

The original sentence sounds a little more descriptive and nuanced. It suggests that calmness emerges gradually as an inner sensation.

So the simpler version is possible, but the original has a more natural sense of a feeling arising.

Because the structure is built around the noun ощущение:

• ощущение чего? = a feeling of what?

So Russian uses another noun:

• ощущение спокойствия = a feeling of calm

If you used the adjective спокойный, you would need a different sentence structure, for example:

• После прогулки в парке я становлюсь спокойнее.
  = After a walk in the park, I become calmer.

So the noun спокойствие fits the grammar of ощущение much better here.

It is a very natural way, but not the only one.

Here are some close alternatives:

• прогулка в парке = a walk in the park
• прогулка по парку = a walk through / around the park

The difference is small:

• в парке emphasizes the location: in the park
• по парку emphasizes movement around the area: through the park / around the park

So your sentence could also be:

• После прогулки по парку у меня появляется ощущение спокойствия.

That would also sound natural.