Extended Data Fig. 10: Odour velocity in model of turbulent plumes points outward from plume centerline and is computed by local space-time correlators.

We use a simple packet model of turbulent plumes. Packets are released from a source and disperse in the lateral direction while being advected downwind (see Methods for model and calculation details). a, Packet velocity \({\langle v\rangle }_{y,t}\) in the plume model, as a function of  \(\bar{y}=y/\sqrt{T}\), for two correlation times, \(T=0.2\) (purple) and \(T=1\) (green), at a fixed time \(t=4\). Here, \(v\) is set to 1. To directly compare velocity for plumes with different T, (and therefore different diffusivities) we plot the velocity versus the normalized length \(\bar{y}\). Specifically, since \(\left\langle {y}^{2}\right\rangle =2T{v}^{2}t\) for \(t\gg T\) then at a given \(t\), the packet distribution in terms of  \(\bar{y}\) is the same for plumes with distinct \(T\). The distribution of packets for either \(T\) is a function of  \(\bar{y}\) shown in grey. The velocity is an odd function of \(y\), i.e. it points outward from the plume axis. In addition, the asymmetry is steeper for higher correlation times. b, The value of the correlator \(\left\langle {\rm{C}}\left(\Delta y,\Delta t|y,t\right)\right\rangle \)as a function of lateral distance \(y\), for various times \(t\) for \(T=0.1\) (left) and \(T=0.3\) (right). Here, \({D}_{p}=0.005\). Since the packets are advected downwind with a velocity \(U\gg v\), the time axis is proportional to the downwind distance. The packet distribution is shown on the bottom; the limits of the \(y\)-axis are chosen such that the plume extents are the same in both plots. c, The total y-integral of the absolute value of \(\left\langle {\rm{C}}\left(\Delta y,\Delta t|y,t\right)\right\rangle \) at a fixed \(t=4\), as a function of odour packet speed (\(y\)-axis) and molecular diffusivity (\({D}_{p}\)), with \(T=1\), \(v=1\). This integral indicates the degree of directional sensing on average. The integral is highest for greater packet speeds and lower molecular diffusivities (top left corner).