On the Effects of Viscosity on the Shock Waves for a Hydrodynamical Case—Part I: Basic Mechanism

<table>Behaviour of the<svg height="15.25" id="M41" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 35.575001 15.25" width="35.575001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g>
<g transform="matrix(.012,-0,0,-.012,23.513,15.187)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>as a function of <svg height="15.25" id="M42" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 29.9 15.25" width="29.9" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M631 18l-4 -26q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -63 14 -77.5t74 -19.5v-28h-262v28q62 5 76 19.5t14 77.5v402q0 62 -13 76t-73 19v28h248q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172q27 -52 89 -144
q49 -71 81 -104q31 -36 72 -47zM212 316h48q73 0 108 29q55 42 55 124q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247z" id="x52"></path></g><g transform="matrix(.017,-0,0,-.017,10.619,11.112)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g>
<g transform="matrix(.012,-0,0,-.012,17.838,15.187)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>for different values of<svg height="15.25" id="M43" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 29.475 15.25" width="29.475" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,11.112)"><path d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28
q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" id="x1D440"></path></g>
<g transform="matrix(.012,-0,0,-.012,23.088,15.187)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>.</table>

Advances in Astronomy

fig1

Figure 1

Figure 1: On the Effects of Viscosity on the Shock Waves for a Hydrodynamical Case—Part I: Basic Mechanism 