This content will become publicly available on July 10, 2024
 Award ID(s):
 1830071
 NSFPAR ID:
 10437708
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 966
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Turbulence and mixing in a nearbottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zeroslope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zerovelocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the nonsloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slopeparallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.more » « less

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The interplay between viscoelasticity and inertia in dilute polymer solutions at high deformation rates can result in inertioelastic instabilities. The nonlinear evolution of these instabilities generates a state of turbulence with significantly different spatiotemporal features compared to Newtonian turbulence, termed elastoinertial turbulence (EIT). We ex plore EIT by studying the dynamics of a submerged planar jet of a dilute aqueous polymer solution injected into a quiescent tank of water using a combination of schlieren imaging and laser Doppler velocimetry (LDV). We show how fluid elasticity has a nonmonotonic effect on the jet stability depending on its magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. In agreement with linear stability analyses of viscoelastic jets, an inertioelastic shearlayer instability emerges near the edge of the jet for small levels of elasticity, independent of bulk undulations in the fluid column. The growth of this disturbance mode destabilizes the flow, resulting in a turbulence transition at lower Reynolds numbers and closer to the nozzle compared to the conditions required for the transition to turbulence in a Newtonian jet. Increasing the fluid elasticity merges the shearlayer instability into a bulk instability of the jet column. In this regime, elastic tensile stresses generated in the shear layer act as an “elastic membrane” that partially stabilizes the flow, retarding the transition to turbulence to higher levels of inertia and greater distances from the nozzle. In the fully turbulent state far from the nozzle, planar viscoelastic jets exhibit unique spatiotemporal features associated with EIT. The timeaveraged angle of jet spreading, an Eulerian measure of the degree of entrainment, and the centerline velocity of the jets both evolve selfsimilarly with distance from the nozzle. The autocovariance of the schlieren images in the fully turbulent region of the jets shows coherent structures that are elongated in the streamwise direction, consistent with the suppression of streamwise vortices by elastic stresses. These coherent structures give a higher spectral energy to small frequency modes in EIT characterized by LDV measurements of the velocity fluctuations at the jet centerline. Finally, our LDV measurements reveal a frequency spectrum characterized by a −3 powerlaw exponent, different from the wellknown −5/3 powerlaw exponent characteristic of Newtonian turbulence.more » « less