Interaction between a Vertical Turbulent Jet and a Thermocline

Abstract

The behavior of an axisymmetric vertical turbulent jet in an unconfined stratified environment is studied by means of well-resolved, large-eddy simulations. The stratification is two uniform layers separated by a thermocline. This study considers two cases: when the thermocline thickness is small and on the order of the jet diameter at the thermocline entrance. The Froude number of the jet at the thermocline varies from 0.6 to 1.9, corresponding to the class of weak fountains. The mean jet penetration, stratified turbulent entrainment, jet oscillations, and the generation of internal waves are examined. The mean jet penetration is predicted well by a simple model based on the conservation of the source energy in the thermocline. The entrainment coefficient for the thin thermocline is consistent with the theoretical model for a two-layer stratification with a sharp interface, while for the thick thermocline entrainment is larger at low Froude numbers. The data reveal the presence of a secondary horizontal flow in the upper part of the thick thermocline, resulting in the entrainment of fluid from the thermocline rather than from the upper stratification layer. The spectra of the jet oscillations in the thermocline display two peaks, at the same frequencies for both stratifications at fixed Froude number. For the thick thermocline, internal waves are generated only at the lower frequency, since the higher peak exceeds the maximal buoyancy frequency. For the thin thermocline, conversely, the spectra of the internal waves show the two peaks at low Froude numbers, whereas only one peak at the lower frequency is observed at higher Froude numbers.

Observations and Modeling of a Hydrothermal Plume in Yellowstone Lake

“…The interaction of the buoyant plume with other processes, such as basin‐scale circulation, seiches, and baroclinic motions, is an intriguing topic, but our survey data lack the spatiotemporal resolution required to resolve these processes (see supporting information S1 for discussion). Buoyant plumes are known to generate internal waves in stratified fluids, including the atmosphere and ocean, through a variety of mechanisms (e.g., Ansong & Sutherland, ; Ezhova et al, ; Fritts & Alexander, ; Lecoanet et al, ). These processes may also be active in lakes, where the enclosed geometry may introduce additional complexities, such as plume‐induced stratification perturbations and forcing of basin‐scale seiches.…”

Numerical Study on Dynamical Structures and the Destratification of Vertical Turbulent Jets in Stratified Environment

“…Rep , 3500 < Re p < 6000 (17) where the Reynolds number at the entrance of pycnocline in this study is defined as Re p = w cp r p /v, and it is detailed in Section 3. The mean data is used to calculate the radial momentum flux dissipation rate with Kh = FLh/FLh5 (Where FLh is the radial momentum flux; FLh5 is the radial momentum flux at R = 5).The radial momentum flux is calculated with an interval of R = 2.5 in the range of R = 5~30.…”

“…With reference to dimensionless parameters of jets in unstratified water, researchers also defined some parameters to study jets in the stratified environment. Ezhova [17] defined the Froude number before the jet reaching the pycnocline Fr t = 0.5U max / R t g , where U max and R t are the maximum velocity and the radius of the jet at the entrance to the thermocline, and studied the penetration height of jets under stratified environment in the range of 0.6 < Fr t < 1.89 by both experimental and numerical simulation. Druzhinin [18] defined the Froude number of the jet as Fr = w 0 /N 0 D 0 , (where w 0 is the initial velocity of the jet; D 0 is the nozzle diameter of the vertical jet; N 0 = g ρ 0 ∆ρ D 0 is the buoyancy frequency at the center of the pycnocline; ρ 0 is the density at the center of the pycnocline; ∆ρ is the density difference between upper and lower layers) and studied the interaction between jets and the pycnocline by DNS.…”

“…The interaction between jets and the pycnocline is studied based on the parameters mentioned above. During the rising process, the density of the jet at the pycnocline entrance is equal to the density of lower layer due to the jet entrains the surrounding fluid [17]. After the jet penetrates the pycnocline, the momentum of the core of upward flow rapidly decays due to negative buoyancy when the jet penetrates through the pycnocline.…”

Spreading height and critical conditions for the collapse of turbulent fountains in stratified media

“…Fountains and plumes are encountered frequently in nature and technical applications such as selective withdrawal, desalination plants, and the replenishment of magma chambers. Since the dynamical behavior of fluids within stratified media presents a problem of considerable interest across a number of fields, turbulent fountains and plumes in uniform and stratified mediums have been the subject of investigation for decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”