Correlations for maximum penetration heights of transitional plane fountains in linearly stratified fluids

Maximum Penetration Height and Intrusion Speed of Weak Symmetric Plane Fountains in Linearly Stratified Fluids

“…This observation is unlike the asymmetric behavior reported for PFs in stratified fluids at larger Fr and Re [10]. This finding implies that for the specific fountain presented, the flow and temperature pattern remains symmetric irrespective of the instant selected in contrast to an asymmetric fountain [10,16,17].…”

“…Similar behavior to that in Figures 1 and 2 can be identified, as fountains stay symmetric and the mixing between the fountain and fluid is minimal. The intrusion again increases significantly compared to the fountain height, especially for a large s. z m reduces with increasing s because of the stabilizing ability of the stratification as discussed in [10,16,17], indicating that s has a notable influence on the MFPH along with the intrusion height.…”

“…Research on PFs in stratified fluids has been scarce and mainly focused on those in turbulent regimes, with z m as the main parameter. In the past several years, we carried out numerical studies on weak and transitional PFs in LSFs to examine their effects on the transition of a PF from symmetric behavior to asymmetric behavior, with z m as the major parameter characterizing the PF behavior [10,[16][17][18]. Nevertheless, the characterization of weak PFs in stratified fluids with small Fr and Re values, in which only the symmetric behavior is present, is currently rarely understood.…”

Characteristics of unsteadiness for transitional plane fountains in linearly stratified fluids

“…The three-dimensional DNS results presented in [1,2] show that over the above-mentioned ranges of F r, Re and s, transitional plane fountains are symmetric in the early developing stage, but become asymmetric and unsteady subsequently. However, the extent of asymmetry and unsteadiness under the influence of F r, Re and s were not studied in [1,2], which motivates the current study to investigate the characteristics of the unsteadiness of the plane fountains over the above-mentioned ranges of F r, Re and s and develop the scaling relations to quantify the unsteadiness.…”

“…This paper is a continuation of our recent study [1,2] in which the asymmetric transition and the maximum fountain penetration heights of transitional plane fountains in linearly stratified fluids were investigated using a series of three-dimensional direct numerical simulations (DNS) obtained by ANSYS Fluent over 25 ≤ Re ≤ 300, 3 ≤ F r ≤ 10 and 0 ≤ s ≤ 0.5. The Reynolds number, Re, the Froude number, F r, and the dimensionless temperature stratification parameter, s, which are the major governing parameters for fountains in linearly stratified fluids, are defined as follows,…”