Gravity currents in a deep anelastic atmosphere

Results are cast in terms of a nondimensional parameter H/H₀ that relates the channel depth H to a scale depth H₀ (the depth at which density goes to zero in an isentropic atmosphere). The classic results based on the incompressible equations correspond to H/H₀ = 0.

For cold gravity currents (at the bottom of a channel), assuming energy-conserving flow, the nondimensional current depth h/H is much smaller, and nondimensional propagation speed C/(gH)½ is slightly smaller as H/H₀ increases. For flows with energy dissipation, C/(gH)½ decreases as H/H₀ increases, even for fixed h/H. The authors conclude that as H/H₀ increases the normalized hydrostatic pressure rise in the cold pool increases near the bottom of the channel, whereas drag decreases near the top of the channel; these changes require gravity currents to propagate slower for steady flow to be maintained.