Fig. 4: Tracers distributions in the patch (salmon color) and at its surrounding waters (blue color).
When the assumption of well-mixed concentrations is taken (top panel), for a given tracer i, we need to specify only its mean concentration in the patch 〈pi(x, t)〉 and at the surrounding 〈si(x, t)〉. Instead, if we account for spatial heterogeneity (bottom panel), second moments of tracers distributions have to be considered, both in the patch \(\langle {p}_{i}^{{\prime} }({{{{{{{\bf{x}}}}}}}},t){p}_{j}^{{\prime} }({{{{{{{\bf{x}}}}}}}},t)\rangle\) and at the surrounding \(\langle {s}_{i}^{{\prime} }({{{{{{{\bf{x}}}}}}}},t){s}_{j}^{{\prime} }({{{{{{{\bf{x}}}}}}}},t)\rangle\), for any i and j.
