Internal gravity waves generated by an impulsive plume

A series of laboratory experiments on the generation of internal waves by a short duration impulsive, turbulent, forced plume descending into a stratified layer has been conducted. After the plume descends to a maximum depth it rebounds to an equilibrium level where the ensuing oscillation results in the generation of a propagating internal wave field. The finite duration impulsive plumes exhibited two classes of behavior: (1) Plumes with a density that matched that of the bottom of the stratified layer had a constant fraction of the plume energy transferred to the internal wave field, with an average value of $E_{\mathrm{IW}}/E_P\cong 6\%$, independent of the duration of the plume release. In contrast, (2) plumes with lower densities, half that of the bottom of the stratified layer, exhibited a larger degree of coupling of the plume energy to the internal wave field that increased with the duration of the plume release, having an average value of $\cong 10\%$. The observed degree of internal wave energy coupling for impulsive plumes is in general agreement with prior studies of continuous convective plumes and descending buoyant parcels.

Figure 1

Schematic of experimental configuration.

Figure 2

Turbulent plume time evolution as captured by the fluorescent dye and artificially colored based on intensity. Data shown are from series C, run 12: $H=11.9\mathrm{cm}$, $N=0.95{\mathrm{s}}^{-1}$, ${\rho }_{\mathrm{r}}=1.17$, $\mathrm{\Delta }T=1.73\mathrm{s}$, $z_{max}=31.2\mathrm{cm}$, and $z_n=11.1\mathrm{cm}$. Successive images are $\mathrm{\Delta }T=0.5,2,5,7,11$, and $13\mathrm{s}$. $z_{max}$ and $z_n$ are shown by the dashed lines in panels 3 and 5, respectively.

Figure 3

Plume width as a function of depth and time, evaluated over a cross-sectional window of 17.2 cm. (a) Series C, run 19: $H=14.0\mathrm{cm}$, ${\rho }_{\mathrm{r}}=1.49$, $\mathrm{\Delta }T=1.68\mathrm{s}$, $z_{max}=35.3\mathrm{cm}$, and $z_n=16.7\mathrm{cm}$. (b) Series B, run 66: $H=21.7\mathrm{cm}$, ${\rho }_{\mathrm{r}}=0.58$, $\mathrm{\Delta }T=1.83\mathrm{s}$, $z_{max}=28.2\mathrm{cm}$, and $z_n=17.9\mathrm{cm}$.

Figure 4

Plume maximum depth vs release duration.

Figure 5

(a) Plume neutral buoyancy depth vs release duration. (b) Plume neutral buoyancy depth scaled by intrinsic scales.

Figure 6

(a) Plume energy vs release duration. (b) Internal wave energy vs release duration.

Figure 7

Internal wave displacements and cumulative energy within the stratified layer. (a,b) Series A, run 3B: $H=21.5\mathrm{cm}$, ${\rho }_{\mathrm{r}}=1.31$, and $\mathrm{\Delta }T=1.62\mathrm{s}$. (c,d) Series D, run 84: $H=12.3\mathrm{cm}$, ${\rho }_{\mathrm{r}}=0.44$, and $\mathrm{\Delta }T=1.25\mathrm{s}$. Wave displacements in (a,c) are scaled by a factor of 5, for clarity.

Figure 8

Energy ratio. (a) ${\rho }_r\cong 1$; (b) ${\rho }_r\cong 0.5$.