The search works as a filter, so without a filter the default is to return no results.
If you wanted a blank search to return no results, one option might be to automatically populate with a value that would have no result on the top of the results page:
<?php
if (isset($_POST['keywords"]) && $_POST['keywords"] == "") {
$_POST['keywords"] = "zznoresultszz";
}
?>
if this was added to the top of your results page and a field named "keywords" was submitted in your search it would search for "zznoresultszz" instead of a blank search and would return no results.