Whatever constricts an orifice, whatever dilates a cavity, whatever establishes an orifice or cavity where none shall be, will disturb the even flow of blood and produce vibrations and a murmur.
—Samuel Jones Gee (1839–1911)
Turbulent blood flow is classically detected by auscultation (listening). Turbulent flow across the valves of the heart causes murmurs. A certain amount of external pressure applied to a brachial artery allows turbulent flow, which you can hear, which is how you measure blood pressure. Carotid bruit's are a sound produced by turbulence in the carotid artery. You can reference any physical examination textbook, e.g., Bate's for information on this method of detecting turbulent flow. There's an NCBI books Clinical Methods textbook that you can search for turbulence.
Turbulence can also be detected by one of a variety of ultrasound methods. The specific measurements taken using these methods are typically anatomic measurements (e.g., thickness of a tissue, distance across a valve), peak flow, overall direction of flow, and gradient measurements, since those are the markers that have been used to characterize disease and/or outcomes. However they can detect turbulence. Quantitative measurements of turbulence just aren't used experimentally.