The search architecture in SharePoint 2013 has changed quite a bit when compared to SharePoint 2010. In fact the Search Service in SharePoint 2013 is completely overhauled. It is a combination of FAST Search and SharePoint Search components.

As you can see the query and crawl topologies are merged into a single topology, simply called "Search topology". Provisioning of the search service application creates 4 databases:

• SP2013_Enterprise_Search - This is a search administration database. It contains configuration and topology information

• SP2013_Enterprise_Search_AnalyticsReportingStore - This database stores the result of usage analysis

• SP2013_Enterprise_Search_CrawlStore - The crawl database contains detailed tracking and historical information about crawled items

• SP2013_Enterprise_Search_LinksStore - Stores the information extracted by the content processing component and also stores click-through information

# Create a new Search Service Application in SharePoint 2013

Add-PSSnapin Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue

# Settings
$IndexLocation = "C:\Data\Search15Index” #Location must be empty, will be deleted during the process!
$SearchAppPoolName = "Search App Pool"
$SearchAppPoolAccountName = "Contoso\administrator"
$SearchServerName = (Get-ChildItem env:computername).value
$SearchServiceName = "Search15"
$SearchServiceProxyName = "Search15 Proxy"
$DatabaseName = "Search15_ADminDB"
Write-Host -ForegroundColor Yellow "Checking if Search Application Pool exists"
$SPAppPool = Get-SPServiceApplicationPool -Identity $SearchAppPoolName -ErrorAction SilentlyContinue

if (!$SPAppPool)
{
    Write-Host -ForegroundColor Green "Creating Search Application Pool"
    $spAppPool = New-SPServiceApplicationPool -Name $SearchAppPoolName -Account $SearchAppPoolAccountName -Verbose
}

# Start Services search service instance
Write-host "Start Search Service instances...."
Start-SPEnterpriseSearchServiceInstance $SearchServerName -ErrorAction SilentlyContinue
Start-SPEnterpriseSearchQueryAndSiteSettingsServiceInstance $SearchServerName -ErrorAction SilentlyContinue

Write-Host -ForegroundColor Yellow "Checking if Search Service Application exists"
$ServiceApplication = Get-SPEnterpriseSearchServiceApplication -Identity $SearchServiceName -ErrorAction SilentlyContinue

if (!$ServiceApplication)
{
    Write-Host -ForegroundColor Green "Creating Search Service Application"
    $ServiceApplication = New-SPEnterpriseSearchServiceApplication -Partitioned -Name $SearchServiceName -ApplicationPool $spAppPool.Name 
-DatabaseName $DatabaseName
}

Write-Host -ForegroundColor Yellow "Checking if Search Service Application Proxy exists"
$Proxy = Get-SPEnterpriseSearchServiceApplicationProxy -Identity $SearchServiceProxyName -ErrorAction SilentlyContinue

if (!$Proxy)
{
    Write-Host -ForegroundColor Green "Creating Search Service Application Proxy"
    New-SPEnterpriseSearchServiceApplicationProxy -Partitioned -Name $SearchServiceProxyName -SearchApplication $ServiceApplication
}

$ServiceApplication.ActiveTopology
Write-Host $ServiceApplication.ActiveTopology

# Clone the default Topology (which is empty) and create a new one and then activate it
Write-Host "Configuring Search Component Topology...."
$clone = $ServiceApplication.ActiveTopology.Clone()
$SSI = Get-SPEnterpriseSearchServiceInstance -local
New-SPEnterpriseSearchAdminComponent –SearchTopology $clone -SearchServiceInstance $SSI
New-SPEnterpriseSearchContentProcessingComponent –SearchTopology $clone -SearchServiceInstance $SSI
New-SPEnterpriseSearchAnalyticsProcessingComponent –SearchTopology $clone -SearchServiceInstance $SSI
New-SPEnterpriseSearchCrawlComponent –SearchTopology $clone -SearchServiceInstance $SSI

Remove-Item -Recurse -Force -LiteralPath $IndexLocation -ErrorAction SilentlyContinue
mkdir -Path $IndexLocation -Force

New-SPEnterpriseSearchIndexComponent –SearchTopology $clone -SearchServiceInstance $SSI -RootDirectory $IndexLocation
New-SPEnterpriseSearchQueryProcessingComponent –SearchTopology $clone -SearchServiceInstance $SSI
$clone.Activate()

Write-host "Your search service application $SearchServiceName is now ready"

See the following articles for information about Search Service Application in SharePoint 2013

• Create and configure a Search service application in SharePoint Server 2013 for information on how to create and configure a Search Service Application
• SharePoint 2013: How to configure Search Services Application (TechNet Wiki)