SQL server disk write queue dramatically grows sometimes
Sounds like you have:


A very crappy IO subsystem.
A checkpoint occurring.
Crappy IO subsystem + checkpoint = high disk queue.



  I found that writing to log (not to data file) is default behavior of
  Full recovery mode. And log can only be copied to data file by Backup
  Transaction Log operation.


No, not really. Your information or understanding is at fault.

Regardless of recovery model, SQL Server uses write-ahead-logging (WAL). An update/delete/insert results in a change to the in-memory data page + a record of the change written to the transaction log. The data page modification is not immediately flushed to the data file. To all intents and purposes you can consider the log write to disk to be immediate (beneath the covers the log is flushed every 60K or on a COMMIT).

What you are seeing when the IO spikes is those data page modifications being flushed to disk as a result of a checkpoint operation.


  A checkpoint writes the current in-memory modified pages (known as
  dirty pages) and transaction log information from memory to disk and,
  also, records information about the transaction log. [Source]


Relevant past questions that may help you understand the mechanics:


SQL Server Cache Flush and Disk I/O
When do you remove entries from a write-ahead log (WAL)?