Penetration height of weak axisymmetric fountain in homogeneous fluid under the combined temperature and salinity effect

Fountains under combined temperature and salinity effect are common in environmental and industrial settings. The behavior of weak axisymmetric fountains under combined temperature and salinity effect is studied with two-dimensional direct numerical simulations over 0.25 ≤ FrT ≤ 2.0 and −0.75 ≤ N ≤ 5.0, where FrT is the Froude number based on temperature only and N is the buoyancy ratio quantifying the ratio of salinity to temperature contributed to density. The results show that for each FrT, both the initial and time-average maximum fountain heights decrease when N increases as the combined negative buoyancy due to both temperature and salinity is strengthened, whereas as FrT increases, they increase as the overall negative buoyancy reduces. If the overall Froude number, Fr, which is based on density due to the combined temperature and salinity contributions, is used instead of FrT, the existing scaling relations for weak axisymmetric fountains with density coming from temperature only are also applicable for the weak axisymmetric fountains under the combined temperature and salinity effect when Fr ≲ 2.0, although there are slight differences in their quantified correlations due to the extra effect from the co-existing salinity. It is further shown that the effect from the co-existing salinity shifts the scaling relation for intermediate fountains with 2.0 ≲ Fr ≲ 4.0 with density from only one contributor to the scaling relation for weak fountains with Fr ≲ 2.0 with density coming from both temperature and salinity, further showing the additional effect of salinity.