Submitting the form actually reloads the page, which is what's causing this illusion of jumping to the top of the page. There are 2 things you can do to counteract this.
1) Similar to what Weedpacket suggested, place an anchor tag with a specific name on your page where you want the page "to be" after you submit the form. In the form's action attribute, append #whatever_the_anchor_tag_is.
For example, if the anchor was <a name="notes"></a> then you'd want to append #notes.
2) A little fancier (and more involved) is to use JavaScript (namely jQuery) to make an AJAX call that does what ever the form does. Using this with event.preventDefault() will stop the page from "jumping" to the top.
Good luck!