User simulation is a potential solution for evaluating conversational search (CS) systems. While existing work focuses on building user simulators by in-context learning with large language models (LLMs) or fine-tuning LLMs, the work of exploring the zero-shot ability of LLM-based user simulators is limited. To this end, we leverage LLMs with zero-shot learning to simulate specific users, given conversational context and user profiles. Furthermore, our proposed LLM-based user simulators are not limited by a single response strategy, such as providing answers or feedback. More specifically, we simulate different users in two different settings. The golden setting only generates a single response based on the predefined trajectory of a conversation. The interactive setting considers the engagement between the CS system and a LLM-based user simulator; moreover, we rely on ReAct, a popular agent framework, to build the CS system. We evaluate utterances generated by LLM-based user simulators on two datasets across several dimensions, such as lexical diversity and readability. Experimental results show several key findings: (i) LLM-generated utterances tend to show higher lexical diversity, (ii) LLM-generated utterances frequently demonstrate higher syntactic complexity, and (iii) LLM-generated utterances require higher reading proficiency, compared to human-generated ones.