ListAndDownloadAzureBlobContentByPrefix.ps1

Login-AzureRmAccount

$containerName = <<string containing container name>>
$storageContext = New-AzureStorageContext -ConnectionString <<connection string to storage account>>
$localDestinationPath = <<string containing file system path.>>
$blobPrefix = <<string containing prefix to search. wildcard character not needed after prefix.>>

#List
#Get-AzureStorageBlob -Context $storageContext -Container $containerName -Prefix $blobPrefix

#List and Download
Get-AzureStorageBlob -Context $storageContext -Container $containerName -Prefix $blobPrefix | ForEach-Object {Get-AzureStorageBlobContent -context $storageContext -Container $containerName -Blob $_.Name -Destination $localDestinationPath -Force}