Abstract
We consider a gravity current released from a lock into an ambient fluid of smaller density, that, from the beginning or after some horizontal propagation X1, propagates along an inclined (up- or down-) bottom. The flow (assumed in the inertial-buoyancy regime) is modeled by the shallow-water (SW) equations with a jump condition applied at the nose (front). The behavior of the current is dominated by the slope angle, θ, but is also affected by additional dimensionless parameters: the aspect ratio of the lock x0/h0, the height ratio of the ambient to lock, H/h0, and the distance of the backwall from the beginning of the slope, X1/x0. We show that the stability of the interface, reflected by the value of the bulk Richardson number, Ri, is essential in the interpretation and modeling. In the upslope flow, Ri increases and hence entrainment/mixing effects are unimportant. In the downslope flow, the current first accelerates and Ri decreases; this enhances entrainment and drag, which then decelerate the current. We show that the accelerating-decelerating downstream current is reproduced well by a SW model combined with a simple closure for the entrainment and drag. A comparison of the theoretical results with previously published experimental data for both upslope flow and downslope flow show fair agreement.
Highlights
Gravity currents (GCs) are ubiquitous in many geophysical and environmental flow such as salt intrusions into lakes and estuaries, glacial runoff into the ocean, turbidity currents in coastal regions, cold downhill airflow in mountain areas, or snow avalanches
We argue that the extended SW model performs well
CONCLUDING REMARKS We have revisited the problem of a gravity current of fixe volume released from a lock, which encounters a downslope or upslope bottom, in the inertial-buoyancy regime
Summary
Gravity currents (GCs) are ubiquitous in many geophysical and environmental flow such as salt intrusions into lakes and estuaries, glacial runoff into the ocean, turbidity currents in coastal regions, cold downhill airflow in mountain areas, or snow avalanches. 22 and 8) reveal that in downslope flow the current firs accelerates and decelerates These observations are routinely compared with the model (referred to as “power law” or “thermal theory”) of Ref. 3 xN ≙ ξ0 +K(g′h0x0)1/3(t + τ0)2/3 (dimensional), where ξ0, τ0 are adjustable constants, and the dimensionless K is given by a formula which contains the entrainment and drag coefficient E, Cd and some adjustable shape-factors. Thermal theory describes both the acceleration phase and the equilibrium state of the current; the common approach is based on a balance between the momentum and mass conservation equations of the finit volume released gravity current.
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