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The present work is devoted to the numerical study of the stability of shallow jet. The effects of important parameters on the stability behavior for large scale shallow jets are considered and investigated. Connections between the stability theory and observed features reported in the literature are emphasized. The paper aims to discuss these issues.

A linear stability analysis of shallow jet incorporating the effects of bottom topography, bed friction and viscosity has been carried out by using the shallow water stability equation derived from the depth averaged shallow water equations in conjunction with both Chézy and Manning resistance formulae. Effects of the following main factors on the stability of shallow water jets are examined: Rossby number, bottom friction number, Reynolds number, topographic parameters, base velocity profile and resistance model. Special attention has been paid to the Coriolis effects on the jet stability by limiting the rotation number in the range of Ro∈[0, 1.0].

It is found that the Rossby number may either amplify or attenuate the growth of the flow instability depending on the values of the topographic parameters. There is a regime where the near cancellation of Coriolis effects due to other relevant parameters influences is responsible for enhancement of stability. The instability can be suppressed by the bottom friction when the bottom friction number is large enough. The amplification rate may become sensitive to the relatively small Reynolds number. The stability region using the Manning formula is larger than that using the Chézy formula. The combination of these effects may stabilize or destabilize the shallow jet flow. These results of the stability analysis are compared with those from the literature.

Results of linear stability analysis on shallow jets along roughness bottom bed are presented. Different from the previous studies, this paper includes the effects of bottom topography, Rossby number, Reynolds number, resistance formula and bed friction. It is found that the influence of Reynolds number on the stability of the jet is notable for relative small value. Therefore, it is important to experimental investigators that the viscosity should be considered with comparison to the results from inviscid assumption. In contrast with the classical analysis, the use of multi-parameters of the base velocity and topographic profile gives an extension to the jet stability analysis. To characterize the large scale motion, besides the bottom friction as proposed in the related literature, the Reynolds number Re, Rossby number Ro, the topographic parameters and parameters controlling base velocity profile may also be important to the stability analysis of shallow jet flows.

The purpose of this study is to use the grounded theory to summarize the types of celebrity persona and to construct a theoretical model for celebrity persona on consumer purchase intention. Based on the study results, it provides better suggestions for merchants and live streamers and is an expansion of previous research on live-streaming e-commerce.

The grounded theory is recognized as the most scientific qualitative research method and is the ideal explorative method for generating theory. First, the participants were interviewed, and interview data were collected. Then the interview data were organized and analyzed. Finally, this paper summarizes the types of celebrity persona and constructes a theoretical model framework of celebrity persona on consumers' purchase intention.

The results show that the celebrity live streamer persona can be divided into two types: personalized persona and professional persona. Through emotional attachment, the celebrity's persona affects the consumer's purchase intentions. As well as, product type plays a moderating role between celebrity persona and consumer purchase intentions.

The contribution of this research is to start from the celebrity persona, link the celebrity persona with the consumer purchase intentions and expand the research scope of the celebrity persona. It opens the “black box” of the heterogeneity of celebrity live streamers' characteristics on consumer purchase intentions.