This isn’t a theme or even a WordPress issue in essence; it’s just how links work. I can however suggest a workaround that might work for you. It may be perceived as breaking the expected behaviour of links for visitors however, and a different approach such as having a tall header image for the home page only and a much smaller header for every other page may be preferable.
When you are linking to a particular page it will always load the full page by default – displaying it from the top. However you can target a link to go to a particular part of a page by linking to the id of a specific element on that page.
Your theme (assuming the site you are referring to is the one listed in your profile, http://reemalhashmi.com) has an id specified for an element enclosing the the menu. This is #site-navigation and we can target a link to go to that id so that any link to another page with the suffix #site-navigation on the link target will go to the navigation rather than the top of the page.
To be able to change the links on your menu you would have to be using a custom menu, and instead of adding the pages as page menu items, you would meed to enter them as link menu items (in WP 3.6 terminology) where you can manually enter the target url of the menu item.
As an example the link to your digital art page in the menu would have the target URL specified as http://reemalhashmi.com/my-art/digital-art#site-navigation selecting this menu item will show the page starting from the #site-navigation element, so the header will initially be off-screen.
