  Gravity currents descending a slope in a linearly stratified environment can
be frequently encountered in nature. However, few studies have quantitatively
investigated the evolution process of lock-exchange gravity currents in such
environments. A new set of analytical formulae is proposed by integrating both
mass conservation and linear momentum equations to determine the front velocity
and the front location of a downslope current. Based on the thermal theory, the
formula considers the influence of ambient stratification by introducing a
newly defined stratification coefficient in the acceleration stage. As for the
deceleration stage, the formula is derived by adding a parameter that takes
into account the density distribution of the ambient water. The transition
point between the acceleration and deceleration stages and the maximum front
velocity are also determined by the proposed formulae. Lock-exchange gravity
current experiments are conducted in the flume with linear stratifications to
provide data for the validation of the formulae. The comparisons between the
calculated and measured data in terms of front location and front velocity show
satisfactory agreements, which reveal that front velocity presents a rapid
acceleration stage and then a deceleration stage in a linearly stratified
ambient.
