A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/jam/volume-2019/3084394/figures/3084394.fig.005a.svgz" name="3084394.fig.005a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>z-component of vorticity <svg height="8.68572pt" id="M540" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.97754 8.68572" width="9.97754pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/jam/volume-2019/3084394/figures/3084394.fig.005b.svgz" name="3084394.fig.005b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>u velocity component</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/jam/volume-2019/3084394/figures/3084394.fig.005c.svgz" name="3084394.fig.005c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>v velocity component</td></tr></table>

<div>The Contours plots of <span class="nowrap"><svg height="6.44133pt" id="M533" style="vertical-align:-0.29774pt" version="1.1" viewbox="-0.0498162 -6.14359 6.59789 6.44133" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"></path></g></svg>-</span>component of vorticity, <svg height="6.1673pt" id="M534" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.11985 6.1673" width="7.11985pt" 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258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z"></path></g></svg> velocity components for <svg height="8.97279pt" id="M536" style="vertical-align:-0.2324896pt" version="1.1" viewbox="-0.0498162 -8.7403 14.4402 8.97279" width="14.4402pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M42 650V615C112 608 121 601 121 516V133C121 48 112 41 37 34V0H347V34C262 41 253 48 253 133V271L321 254C332 254 347 254 362 256C468 269 567 330 567 464C567 529 540 579 493 611C453 639 397 650 318 650H42ZM253 570C253 585 255 595 262 601C268 606 280 611 299 611C360 611 423 574 423 461C423 326 343 300 307 300C286 300 265 305 253 310V570Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.787,0)"><path d="M306 382C339 403 362 417 379 433C398 450 411 473 411 500C411 578 352 635 248 635H247C181 635 134 604 106 573L56 506L82 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Journal of Applied Mathematics

fig5

Figure 5

Figure 5: A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations 

Figure 5 | A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations 