This research by "think with Google" titled "Principles of Mobile App Design: Engage Users and Drive Conversions" from March 2016, gives a series of principles for apps usability based on studies of "more than 100 people on 100 different apps".
We partnered with AnswerLab to conduct a user study of more than 100 people on 100 different apps across a variety of verticals including e-commerce, insurance, travel, food ordering, ticket sales and services, and financial management. (Gaming apps, social networking apps and music services were not included in the study.)
The study is focused on Mobile apps.
As many as 25% of app users open an app once and never return (Source: eMarketer “App Marketing 2015: Fighting for Downloads and Attention in a Crowded Market,” July 2015).
More than ever, people are engaging with their phones in crucial moments and for shorter periods of time. Their experiences need to be efficient and delightful. Plus, a well-designed app that provides utility has the power to cut through the clutter. It can deliver on people’s many I-want-to-know, I-want-to-go, I-want-to-buy, and I-want-to-do moments.
This point is significant to the search box display in Mobile apps:
In-App Search
Effective and useful app search is crucial for helping app users find what they need. (...)
6. Prominently display the search field.
Users with a specific task or need will typically look for a search field. They often prefer this to browsing. Apps that do not have a prominently placed search box can cause user frustration and slow the user down.
Don't:
The search functionality is hidden behind a menu option.
Do:
An exposed search field is easily located.
I only included the point relevant to the search box. Other points in the document include principles about search results, search filtering, etc.