Analytical Solutions of the Balance Equation for the Scalar Variance in One-Dimensional Turbulent Flows under Stationary Conditions

<div>Normalized solutions of the mean concentration and its gradient for a continuous plane source, only considering the advection term and a 0th order kinetics (<svg height="9.21094pt" id="M205" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 32.0662 9.21094" width="32.0662pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z" id="g113-86"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="727" vert-adv-y="727"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,13.638,0)"><path d="M535 323V373H52V323H535ZM535 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Advances in Mathematical Physics

fig6

Figure 6

Figure 6: Analytical Solutions of the Balance Equation for the Scalar Variance in One-Dimensional Turbulent Flows under Stationary Conditions 