{"product_id":"9783540160311","title":"The Shallow Water Wave Equations: Formulation, Analysis and Application","description":"\u003ch1\u003eThe Shallow Water Wave Equations: Formulation, Analysis and Application\u003c\/h1\u003e \u003ch2\u003eKinnmark, Ingemar\u003c\/h2\u003e \u003cp\u003e1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo­ mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M(\"vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L\/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2\/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele­ ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1985-11-01\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540160311\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-82646-7\u003c\/p\u003e \u003cp\u003eDimensions: 244.0cm x170.0cm\u003c\/p\u003e \u003cp\u003ePages: 188.0\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44422509330572,"sku":"9783540160311","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540160311.jpg?v=1756268635","url":"https:\/\/lateknightbooks.com\/products\/9783540160311","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}