Intrusion Flow Into a Density Stratified Reservoir

Dense underflow into a lake or reservoir – supercritical flow solutions

“…The result ( 24) is now a singular integral equation for δ b , but it is no longer singular at the end points. Our solution strategy is mostly the same as that used in [13,23,24] and the integral equation ( 24) can be solved by transforming it to the airfoil equation using s = 2 u − 1, giving…”

“…Although this angle can be found numerically by using standard numerical techniques, a semi-analytic solution to this integral can be found by using a result from Glauert [26] and Tricomi [22]. Details of this process are given in Omar [24].…”

“…After some fairly involved calculations (see Omar [24]) we can also compute the value of τ (0) to be…”

“…In the model used in this work there are only two different types of separation point, one in which the interface separates smoothly, and the other in which the surface forms a stagnation point at separation [14,24]. We…”

“…It is possible to show [24] that the only possible values for the angles between the side of the solid wall and the free surface are 2π 3 or −π. The −π case corresponds to the interface leaving horizontally, while the 2π 3 case corresponds to the interface leaving the solid wall at an angle γ = α − π 3 making a simple corner.…”