Thin Unsteady Heavy Jets

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Thin Unsteady Heavy Jets
Joseph B Keller
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From this it follows that "1 ■' z "^ o r. . -i I *- . I; . 1 (2. 3) yi(-, t) = - y2(x, t) Inserting the new variables, equations (2. 2), into equations (2. 1) wo obtain (lotting — = CC ) QTu - V u + V =0 X - ox y y (o) (o) (o) ^ (o) (o) (o) d) -Yot^y - Yox^ ^y ^^ 'y -Py e) y v^°) -f u(°) - ^ox y y f) P^"^ =0 at y = y:°^x, t) g) Yot ^ ^^°^yox = ^^°^ ^^ y = yi°^x, t). The procedure thus far is nearly the same . As that of [2] and [3j" 1'he essential differoncc occiirs in the choice of dimonsionle...ss variables . 3« Zero- Order Solution for Unsteady Jets Prom equations (2, 6b) and (2, 6e) it follows that (1. 1) u^^^ = u^'^^x, t), v(°) = v^°^x, t) . Now using equations (3»1) in (2. 6c), we have p;^ ' = 0, and then from (2. 6f) (3. 2) p^*^) = . With these results, equations ( 2 . 6b) -( 2, 6f ) are identically satisfied, and only equations (2. 6a) and (2. 6g) remain. These equations are Insufficient to complete the determination of the zero order terms, and therefore we proceed to equate to zero the coefficients of - vt vs .

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