Either go to the tiddler $:/themes/jd/Whitespace/template/sidebar
and delete the part related to the search:
<div class="jd-sidebar-column">
<div class="jd-search-wrapper">
<div class="jd-search-header">
<$keyboard class="jd-searchbar-wrapper" tag="div" key="ctrl+space" actions=<<NewTidActions>>>
<$edit-text tiddler="$:/temp/search" type="search" tag="input" placeholder="Search / create" class="jd-searchbar"/>
</$keyboard>
<div class="jd-searchbar-buttons">
<$list filter="[[$:/temp/search]!text[]]">
<$button tooltip="Create new tiddler with this title" class="tc-btn-invisible" actions=<<NewTidActions>>>
{{$:/core/images/new-button}}
</$button>
<$button tooltip="Clear searchbar" class="tc-btn-invisible">
<$action-setfield $tiddler=<<wsconfig search>> text="no"/>
<$action-setfield $tiddler="$:/temp/advancedsearch" text=""/>
<$action-setfield $tiddler="$:/temp/search" text=""/>
{{$:/core/images/close-button}}
</$button>
</$list>
<$list filter="[list[$:/StoryList]] +[field:title[$:/AdvancedSearch]]" emptyMessage=<<control-panel-button>>>
<<control-panel-button "tc-selected">>
</$list>
</div>
</div>
<$reveal state="$:/temp/search" type="nomatch" text="">
<div class="jd-search-results">
<$scrollable fallthrough="no" class="results">
<$set name="searchTiddler" value="$:/temp/search">
<$list filter="[all[shadows+tiddlers]tag[$:/tags/SearchResults]!has[draft.of]butfirst[]limit[1]]" emptyMessage="""
<$list filter="[all[shadows+tiddlers]tag[$:/tags/SearchResults]!has[draft.of]]">
<$transclude/>
</$list>
""">
<$macrocall $name="tabs" tabsList="[all[shadows+tiddlers]tag[$:/tags/SearchResults]!has[draft.of]]" default={{$:/config/SearchResults/Default}}/>
</$list>
</$set>
</$scrollable>
</div>
</$reveal>
</div>
</div>
or use css to hide it. In a tiddler with the tag $:/tags/Stylesheet :
.jd-sidebar div>.jd-sidebar-column{ display:none; }