The river Severn neighbours clashed in October, when Bristol ran out 11-7 winners, but after beating Heineken Cup champions Munster in the Magners League last weekend, Turner said his side must adopt the same no-nonsense approach for Bristol's visit.
He said: "It was a war-zone around the rucks and mauls against Munster and we must expect the same against Bristol.
"Once we get used to that physicality our half-backs are capable of controlling the game, but we must raise our tempo and make sure we come out on top when it comes to winning loose ball on the ground."
After their 19-12 win over Munster last Friday, captain Kevin Morgan says the Dragons must take confidence from their impressive win and show no fear.
The Dragons are just three points behind Pool One leaders Bristol and Morgan says this is the most important game of his 18 months at the Newport-based side.
He commented: "It's a massive game for us if we want to make the quarter-finals; if we want to do anything in this competition we have to win this game.
"They are a very street-wise side with a lot of old hands in the pack and a very tough side to break down. They will want a win to guarantee themselves a home quarter-final.
"We have to concentrate on moving the ball around a bit and play at a high tempo. We shouldn't be afraid of having the Guinness Premiership's top side here, we must have confidence in our own abilities."
With several Welsh internationals in their ranks, Bristol's ex-Wales lock and Neath captain Gareth Llewellyn naturally knows the Dragons players well and can give his side some inside knowledge.
Dragons coach Turner insists Bristol have far more to offer than just a blood and thunder pack, with former All Black fly-half David Hill kicking to the corners.
Turner added: "It's a myth that Bristol are a forward-orientated side as they have a lot of pace out wide in wingers David Lemi and Lee Robinson.
"They have a lot of grunt up front but they do a lot of good, honest work which wins them games. They have a lot of gnarled and experienced players, we have to be just as street-wise."
Newport-Gwent Dragons: K Morgan (capt); G Wyatt, P Emerick, A Smith, A Brew; C Sweeney, A Walker; A Black, K Crawford, L Harrison, I Gough, P Sidoli, A Hall, J Ringer, C Charvis
Replacements: R Wilkes, D Maddocks, M Owen, N Fitsemanu, G Baber, M Hercus, A Thomas
Bristol Rugby: C Morgan; L Robinson, S Cox, S Taumalolo, D Lemi; D Hill, B O'Riordan; D Hilton, M Regan, D Crompton, R Winters, G Llewellyn, A To'oala, M Salter, D Ward-Smith
Replacements: S Nelson, W Thompson, M Sambucetti, C Short, G Nicholls, J Strange, W Pozzebon
Referee: Romain Poite (France)