[jQuery] Triggering a select list from a div onclick

I need to be able to trigger (open) a select list when I click on a
div.

I would love something like this to be possible:

<div onclick="$('select[name="menu"]').open">Click me</div>

<select name="menu" style="display:none">
<option value="option1">Option 1</option>
<option value="option2">Option 2</option>
<option value="option3">Option 3</option>
</select>

Is there anything remotely similar/possible to what I am trying to
achieve?

Thanks, Mat.