To raise the energy efficiency of wireless clients, it is important to sleep in idle periods. When multiple network applications are running concurrently on a single wireless client, packets of each application are sent and received independently, but multiplexed at MAC-level. This uncoordinated behavior makes it difficult to control of sleep timing. In addition, frequent state transitions between active and sleep modes consume non-negligible energy. In this paper, we propose a transport-layer approach that resolves this problem and so reduces energy consumed by multiple TCP flows on a wireless LAN (WLAN) client. The proposed method, called SCTP tunneling, has two key features: flow aggregation and burst transmission. It aggregates multiple TCP flows into a single SCTP association between a wireless client and an access point to control packet transmission and reception timing. Furthermore, to improve the sleep efficiency, SCTP tunneling reduces the number of state transitions by handling multiple packets in a bursty fashion. In this study, we construct a mathematical model of the energy consumed by SCTP tunneling to assess its energy efficiency. Through numerical examples, we show that the proposed method can reduce energy consumption by up to 69%.