Under pressure: turbulent plumes in a uniform crossflow

Direct numerical simulation is used to investigate the integral behaviour of buoyant plumes subjected a uniform crossflow that are infinitely lazy at source. Neither plume trajectory defined by centre mass $z_c$ nor central streamline $z_{U}$ aligned with average streamlines inside plume. Both and shown correlate field lines total buoyancy flux, which implies model for vertical turbulent flux required faithfully predict angle. A study volume conservation equation shows entrainment due incorporation ambient fluid non-zero velocity increase in surface area (the Leibniz term) dominant mechanism strong crossflows. The data indicate pressure differences between top bottom play leading role evolution horizontal momentum balances crucial appropriately modelling rise. By direct parameterisation pressure, an developed good agreement simulations sufficiently crossflow. perturbation expansion current intermediate-range valid downstream distances up $100\ell _b$ – $1000 \ell , where $\ell length scale based on flow speed flux.