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Interaction between a Sine-type Horizontal Shear Flow and Thermal Convections in a Rotating System with a Tilted Axis

Naoaki Saito, Keiichi Ishioka (Graduate School of Sciences, Kyoto University)

(Received 17 July 2009; in revised form 8 September 2009)


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 $ Ta=0$ and $ Ta=10^4$ (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 $ Ta=3\times 10^4$ and $ Ta=10^5$, roll convections in a herringbone pattern are formed. In case of $ Ta=3\times 10^4$, the mean flow is largely accelerated, but in case of $ Ta=10^5$, the acceleration is not significant. Linear stability analyses of the initial field in cases of $ Ta=3\times 10^4$ and $ Ta=10^5$ 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.