Inserting content inside a div using .append()

I am trying to insert content into a div using a jQuery variable.

What I'm trying to get is this.

<div class="results">
  <div class="user-div">
     <p>Hello world</p>
  </div>
</div>

However it is rendering as:

<div class="results">
  <div class="user-div"></div>'
  <p>Hello world</p>
</div>

The following appears to be the correct syntax. It technically works if I use $('.user-div).append() but I'm trying to use a jQuery variable.

var $results = $('.results');
var $userDiv = $results.append('<div class="user-div"></div>')
$userDiv.append('<p>Hello world</p>');

In this case, the problem isn't appending a div to the DOM, but then also appending elements to that div using jQuery variables. Any suggestions are appreciated.