The concept of turbulence has been well-developed by Kritzman and Turkington using a distance function. You want to look at the joint behavior across assets in manner that accounts for both volatility and correlation. From this distance function we can measure the correlation surprise, the impact of changes in the correlation across assets as well as shocks to volatility. The use of distance functions provides simple means of accounting for both volatility and correlation in a single measure of disruption.
Using the turbulence distance function, events can be decomposed into magnitude or correlation blind measures when the off-diagonals are set to zero and correlation surprises which is the ratio of turbulence versus magnitude measures, or volatility shocks and correlation shocks from the turbulence measure.
The turbulence function has been recently used in a paper to measure disruption across a set of large trend-followers. Periods of high turbulence across managers can be matched with market events to determine when diversification across managers is most needed. See "Quantifying Turbulence in Trend-following".
The results suggest that turbulence shocks are associated with specific market events. Some of these events raise volatility across all managers, magnitude shocks while others will be associated with correlation shocks which are likely associated with differences in portfolio compositions across managers. Investors need to be aware of these shocks to build better portfolios. High turbulence will in general show low returns.
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