A. Ishizawa

H. Tsutsui

M.M. ?koric?

N. Nakajima

S. Maeyama

S. Tsuji-Iio

T.-H. Watanabe

National Institute for Fusion Science (NIFS-Repository)

Effects  of  time-varying  sheared  E×B  flow  on turbulence  driven  by  slab  ion  temperature  gradient instabilities  are  investigated  by  means  of  Landau  fluid simulation.  Here,  the  E×B  flow,  which  consists  of stationary and time-periodic oscillatory parts, is externally imposed  to  the  turbulence.  The  dependence  on  the amplitude and frequency of E×B flow is examined in the case that  the amplitude of oscillatory part  is the same or less  than  that  of  stationary  part.  The  ion  heat  transport caused by turbulence oscillates with the same period as the E×B  flow and  the  time-averaged  transport  coefficient  is larger  than the coefficient which is evaluated without the oscillatory  part.  The  time-averaged  coefficient  is maximized when the amplitude of oscillatory part is equal to that  of stationary part.  As the frequency of E×B flow increases,  the  time-averaged  coefficient  decreases  and  is close  to  the  coefficient  which  is  evaluated  without  the oscillatory  part.  This  mechanism  is  explained  by introducing a kind of the logistic equation which describes the time evolution of transport coefficient as a response of turbulence to the amplitude of E×B flow1).Nonlinear  Landau  fluid  simulations  of  the  ITG turbulence with the externally imposed sheared E×B flow were performed to investigate the effects of time-varying shear  flow  on  transport  suppression.  The  E×B  flow  is externally imposed to the turbulence, and its amplitude is given by Aext(t) = As+Ao sin(ωot). We considered the case where the energy of E×B flow is close to or larger than that of  the  turbulence,  and  examined  the  dependence  of  the turbulent heat transport on the amplitude and frequency of E×B  flow.  Figure  1  shows  the  time-averaged  transport coefficients  against  the  amplitude  of  oscillatory  part normalized to the stationary one, Ao/As, for different As. As As increases,  the  time-averaged  coefficient  decreases since the stronger shear  flow is more effective to distort eddies  of  ITG  turbulence.  On  the  other  hand,  as  Ao increases for a fixed As, the time-averaged coefficient rises for As>Ao, but drops for As<Ao. Thus, the time-averaged coefficient has extremal values when As = Ao. The time-averaged  transport  coefficient  is  plotted  in  Fig.  2  as  a function  of  the  frequency of  E×B flow.  The  dotted  line shows the transport coefficient for the stationary E×B flow case.  The  solid  line  represents  the  analytic  solution  of model equation, which is discussed in the next section. The time-averaged  transport  coefficient  decreases  as  the frequency of E×B flow increases, and becomes close to the transport coefficient for the stationary E×B flow case. This indicates  that  the  effect  of  the  oscillation  on  the  time-averaged decreases as the frequency increases.In summary, it  was found that the time-averaged transport coefficient is larger than the transport coefficient in case without oscillation. This implies that the oscillation of  E×B  flow  enhances  the  transport.  This  transport enhancement is attributed to the response of turbulence, as the turbulence grows up when |Aext(t)| is low but decays when  |Aext(t)|  is  high.  The  temporal  variation  in  the transport coefficient is impulsively peaked (not sinusoidal), and  hence,  its  time average  does  not  vanish  so  that  the coefficient is enhanced. The enhancement in the transport is found in the cases with As>Ao. Furthermore, for larger Ao, the transport is maximized when As = Ao (Fig. 1). This is because  the  turbulence  is  enhanced  when the  oscillatory part cancels out the stationary one, and leads to the weak flow shear. Next, we investigated the frequency dependence of  the  heat  transport.  As  the  frequency  of  E×B  flow increases,  the  effect  of  oscillation  on  heat  transport  is weakened, and the transport coefficient is close to the value for  the  case  without  oscillation.  This  is  because  the turbulence follows to the time-varying E×B flow with the delay,  which is characterized by the typical time scale of turbulence such as the growth rate, and cannot keep up with the high frequency oscillation of E×B flow. To mimic the observed properties of the transport coefficient, which has the time delay and impulsive enhancement in its evolution, we introduced  the  logistic-type  equation,  where  a  target value  of  transport  coefficient  was  supposed  to  be determined by the instantaneous value of E×B flow.Fig. 1.  Time-averaged transport coefficient as a function of the amplitude ratio.  Fig. 2.  Time-averaged transport coefficient as a function of the frequency of the ExB flow. As a reference, the transport coefficient evaluated without oscillation is plotted.1)  Maeyama, S, Ishizawa, A., Watanabe, T.-H., Škorić, M. M.,  Nakajima,  N.,  Tsuji-Iio,  S.,  Tsutsui,  H.,  Physics  of Plasmas 49, (2010) 062305.324§4. Effects of Time-varying E×B Flow on Slab Ion-temperature-gradient TurbulenceMaeyama, S. (Tokyo Institute of Technology),  Ishizawa, A., Watanabe, T.-H., Škoric´, M.M.,  Nakajima, N.,  Tsuji-Iio, S., Tsutsui, H. (Tokyo Institute of Technology)

Effects of Time-varying E×B Flow on Slab Ion-temperature-gradient Turbulence

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Effects of Time-varying E×B Flow on Slab Ion-temperature-gradient Turbulence

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