With a low-latitude region of planets in mind, we study thermal convections in a sine-type horizontal shear flow in a rotating system with a tilted axis to explain how the mean flow is accelerated by roll convections in a herringbone pattern.
We perform non-linear time evolutions. In cases of 
and 
(The Taylor number is a measure of the intensity of rotation.), neither roll convections parallel to the mean flow nor those in a herringbone pattern are formed. On the other hand, in cases of
and 
, roll convections in a herringbone pattern are formed. In case of
, the mean flow is largely accelerated, but in case of , the acceleration is not significant. Linear stability analyses of the initial field in cases of
and are also done to show that the herringbone pattern corresponds to the structure of the largest growing eigenmode of the initial field. Analysing second-order effects of the linear eigenmode, we show that contribution of the Colioris force acting on the second-order vertical flow to the acceleration of the mean flow is larger than that of direct momentum transport proposed by Hathaway & Somerville(1987). Further detailed analyses of this effect show that the following process is important. At first, thermal transport by disturbances generates buoyant deviations. Next, the buoyant deviations produce a vertical flow. Finally, the Colioris force acting on the vertical flow accelerates the mean flow.