Both the Indian and Chinese navies are not only growing at a rapid rate but are also operating farther from home. This can be seen by the visit of Chinese and Indian warships to Israel. On August 7th three Indian warships (a destroyer, two frigates, and a supply ship) arrived for a four day visit. On August 12th the Chinese arrived (a destroyer, a frigate, and a supply ship) for a similar visit. The Indian Navy had visited before but this was a first for the Chinese.
Both these visits were a result of several trends and special circumstances. First, there’s Somalia and the anti-piracy patrol (Task Force 151) that has been operating there for nearly a decade. Chinese and Indian warships have been operating independently off Somalia since 2008, while Japanese ships have been operating with Task Force 151. Most warships on anti-piracy duty belong to TF 151. Most of the remainder belongs to the EUNFS (European Union Naval Force Somalia). But some nations continue to operate independently, more or less. There is always some communication, coordination, and sharing of information with TF 151 and EUNFS. Everyone has a chance to see each other in action. This is particularly interesting for China, which has not (in the last five centuries) operated so far from home. The Chinese and the Indians get a chance to check each other out, as both are now vying for supremacy in the Indian Ocean.
The enthusiasm in China for building a larger navy is not aimed at the United States but at the enormous, and growing, vulnerability of its maritime commerce. For example, over 80 percent of the oil China imports comes through the Indian Ocean and the Straits of Malacca. These are the busiest straits in the world (about 130 ships a day). Other nations have an interest in keeping these straits (which are the easiest way of moving between the Indian and Pacific oceans) open: Japan and South Korea, for example. Both, like China, move most of the oil, and much of their trade, through those straights. The nations immediately adjacent to the straits (Singapore, Indonesia, and Malaysia) conduct joint patrols to keep pirates and terrorists under control. But if some other nation wanted to hurt China, all they have to do is block those straits. You could do that by sinking large ships in the narrowest parts of the straits or putting a superior naval force there.
China does not want to be dependent on another nation, be it Japan, South Korea, or the United States for the safety of its maritime commerce. The only way to avoid that humiliating fate is to become the dominant regional naval power. While the Chinese see this as purely a matter of self-defense, China's neighbors see it as an attempt to impose Chinese control over "the eastern Sea" (the western Pacific, waters that China has historically seen as its own) and the Indian Ocean. China is not concerned about any fears its neighbors might have. The leadership in China is only concerned with the well-being of the Chinese economy (which is necessary to keep the Communist Party in power). Thus the eagerness to build a much larger navy and extend Chinese control over areas that have not seen a Chinese warship for centuries.
India is not surrendering the Indian Ocean to the Chinese and is building a fleet capable of confronting Chinese expansion. China’s neighbors in the Western Pacific (especially the South China Sea) are forming a naval coalition to oppose Chinese aggression. The Chinese say they are dissuaded by this.