Select Taxonomy TermSet for site collection navigation using PowerShell

Question

Can someone help me to figure out how to force a certain site collection to start using a term set for navigation?

I already have a prepared term set that can be used for navigation, but I don't want to use GUI to apply it. I am in the process of automating this step. This is a sample code that I've got so far.

Add-PSSnapin microsoft.sharepoint.powershell
function Get-TaxonomySessionDefault()
{
    $centralAdmin = Get-SPWebApplication -IncludeCentralAdministration | Where {$_.IsAdministrationWebApplication} | Get-SPSite
    $session = new-object Microsoft.SharePoint.Taxonomy.TaxonomySession($centralAdmin)
    return $session
}

function Get-TermStoreDefault()
{
    $session = Get-TaxonomySessionDefault
    $serviceApp = Get-SPServiceApplication | Where {$_.TypeName -like "*Metadata*"}
    $termStore = $session.TermStores[$serviceApp.Name]    
    return $termStore;    
}

$termStore = Get-TermStoreDefault
$termGroup = $termStore.Groups["Site Collection - siteUrl.ca-sites-subsite"]
$termSet = $termGroup.TermSets["Subsite Navigation"]
$site = get-spsite "https://siteUrl.ca/sites/subsites"
# How Do I apply $termSet to become $site's navigation?
# Please, note, that $termSet is ready to be used as a navigation term set

Answer 1

Ok, I think, I've got it working:

Add-PSSnapin microsoft.sharepoint.powershell
function Get-TaxonomySessionDefault()
{
    $centralAdmin = Get-SPWebApplication -IncludeCentralAdministration | Where {$_.IsAdministrationWebApplication} | Get-SPSite
    $session = new-object Microsoft.SharePoint.Taxonomy.TaxonomySession($centralAdmin)
    return $session
}

function Get-TermStoreDefault()
{
    $session = Get-TaxonomySessionDefault
    $serviceApp = Get-SPServiceApplication | Where {$_.TypeName -like "*Metadata*"}
    $termStore = $session.TermStores[$serviceApp.Name]    
    return $termStore;    
}

$termStore = Get-TermStoreDefault
$termGroup = $termStore.Groups["Site Collection - siteUrl.ca-sites-subsite"]
$termSet = $termGroup.TermSets["Subsite Navigation"]
$site = get-spsite "https://siteUrl.ca/sites/subsites"

$web = $site.RootWeb
$navigation = $web.Navigation
$pubWeb = [Microsoft.SharePoint.Publishing.PublishingWeb]::GetPublishingWeb($web)
$webNavigationSettings = new-object Microsoft.SharePoint.Publishing.Navigation.WebNavigationSettings -ArgumentList @($web)
$webNavigationSettings.GlobalNavigation.Source = [Microsoft.SharePoint.Publishing.Navigation.StandardNavigationSource]::TaxonomyProvider
$webNavigationSettings.GlobalNavigation.TermStoreId = $termStore.Id;
$webNavigationSettings.GlobalNavigation.TermSetId = $termSet.Id;
$webNavigationSettings.Update()
$pubWeb.Update()