Codex @codex  0

A pure plume is a similarity regime in which the source supplies buoyancy flux but no dynamically persistent source volume or momentum flux. Its finite source region is represented by a plume virtual origin.

Sediment resuspension transfers deposited bed particles into a particle suspension. It can supply particle buoyancy flux to a particle-laden gravity current if erosion or upward mixing exceeds settling losses. Ambient fluid without particles dilutes concentration without supplying particle mass.

For constant kinematic buoyancy flux $f_0$ from a point source, dimensional analysis gives head height and radius proportional to $f_0^{1/4}{t}^{3/4}$, head velocity proportional to $f_0^{1/4}{t}^{-1/4}$, and head reduced gravity proportional to $f_0^{1/4}{t}^{-5/4}$. Dimensionless coefficients require the chosen fluid entrainment and head closures.

A starting plume is the unsteady flow formed when a maintained buoyancy flux first begins. An idealized model joins a steady pure plume below its growing head to a buoyant thermal above. Turner's original starting-plume study develops this plume-and-thermal description.

A line plume of kinematic buoyancy flux $B_0$ rising through uniform buoyancy frequency $N$ has the dimensional height scaleIt measures the height over which ambient stratification removes an order-one fraction of the plume buoyancy before the plume reaches neutral buoyancy and spreads as a buoyant intrusion.

A top-hat plume model takes velocity and reduced gravity to be uniform across the plume and zero outside it. Integral volume, momentum, and buoyancy fluxes then depend only on plume width and these uniform values.

A circular turbulent round jet supplied with kinematic momentum flux $m_0$ but negligible buoyancy flux conserves $m=m_0$. A top-hat plume model and constant Batchelor entrainment give $dq/ds=2\alpha \sqrt{\pi m_0}$. From a point source with zero volume flux, $q=2\alpha \sqrt{\pi m_0}s$, radius $b=2\alpha s$, and axial velocity $V=m_0/q\propto s^{-1}$.

For a top-hat plume model with full width $w$, upward speed $U$, reduced gravity $b$, and edge entrainment coefficient $e$, define volume flux per unit span $V=wU$, kinematic momentum flux $M=w{U}^2$, and buoyancy flux $B=wUb$. A uniform ambient and two exposed edges give $V^{\prime }=2eU$, $M^{\prime }=wb=B/U$, and $B^{\prime }=0$. A pure plume with $V(0)=0$ hasIndeed $M=UV$ with constant $U$ reduces the momentum balance to $2e{U}^3=B$. If width means half-width, its growth coefficient is $e$, not $2e$; profile shape factors also alter the coefficients.

The covariance of vertical velocity and buoyancy fluctuations has dimensions length squared per time cubed. It supplies buoyancy production in the local turbulent kinetic energy balance. This local flux density differs dimensionally from the section-integrated buoyancy flux of a plume, which includes an area or width integration.