Vorticity and circulation: spatial metrics for evaluating flow complexity in stream habitats

Channel topography, formed by boulders, submerged bars, and meanders, creates complex flow patterns. These flow patterns exist over a variety of spatial scales and provide habitat for many aquatic organisms. Spatial flow features cannot be adequately characterized with qualitative descriptions or hydraulic metrics such as depth and velocity. Two-dimensional hydraulic model simulations, based on detailed channel geometry, are used to develop and test vorticity (a point metric) and a circulation-based metric (an area metric) as means of quantifying spatial flows occurring within micro-, meso-, and macro-habitat features. The proposed spatial metrics are computed throughout distinctly different regions of a study site. The vorticity metric produces small absolute values in uniform flows and large absolute values in complex flows. Circulation metric values varied by a factor of 11.7 within distinctly different regions of the modeled study site and suggest that the metric provides a means of quantifying flow complexity within a study reach or within individual mesoscale habitats such as pools, eddies, riffles, and transverse flows. The circulation metric is used to quantify flow complexity around three brown trout (Salmo trutta) redds to provide an example of how the proposed metric might be employed in habitat studies.