[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-672271-105":59,"doc-detail-672271-en":129},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":122,"head_meta":124,"extra_data":126,"updated_unix":128},105,"en","physocea-44115411-a-atmospheric-dynamics-i-key-formulas-and-constants","PHYS/OCEA 4411/5411 A Atmospheric Dynamics I - Key formulas and constants","","Compiled reference sheet for Atmospheric Dynamics, listing core physical constants and standard fluid-dynamics quantities used in the course. Includes dry adiabatic lapse rate, thermodynamic parameters, Earth rotation and Coriolis terms, ideal-gas and potential-temperature relations, hydrostatic and momentum balances, continuity in Z and pressure coordinates, geostrophic and thermal-wind relationships, and circulation/vorticity with potential vorticity formulations, including associated tendencies.",{"@graph":69,"@context":121},[70,84,104],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/physocea-44115411-a-atmospheric-dynamics-i-key-formulas-and-constants/672271/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":98,"encodingFormat":97,"isAccessibleForFree":99,"interactionStatistic":100},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/physocea-44115411-a-atmospheric-dynamics-i-key-formulas-and-constants/672271.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02",true,{"@type":101,"interactionType":102,"userInteractionCount":8},"InteractionCounter",{"@type":103},"ViewAction",{"@type":105,"mainEntity":106},"FAQPage",[107,113,117],{"name":108,"@type":109,"acceptedAnswer":110},"What core atmospheric constants and gas parameters are listed?","Question",{"text":111,"@type":112},"The sheet provides values such as the dry adiabatic lapse rate, the specific heat ratio, gas constant for dry air, and standard gravity, along with Earth-rotation and sea-level reference density and pressure.","Answer",{"name":114,"@type":109,"acceptedAnswer":115},"How are geostrophic and wind relationships expressed?",{"text":116,"@type":112},"It includes geostrophic wind relations on Z and pressure surfaces, plus approximate prognostic equations that connect ageostrophic components to pressure-gradient forcing.",{"name":118,"@type":109,"acceptedAnswer":119},"Which stability and vertical-motion concepts are included?",{"text":120,"@type":112},"It covers potential temperature, buoyancy acceleration and buoyancy frequency, static stability, thickness relations, and links between vertical velocity and continuity in pressure coordinates.","https://schema.org",{"og:url":83,"og:type":123,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":125,"canonical":83},"index,follow",{"doc_id":127,"site_id":62},672271,1793588391,{"code":4,"msg":5,"data":130},{"doc_id":127,"user_id":131,"nickname":92,"user_avatar":132,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":138,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":139,"faqs":140,"seo_title":141,"seo_description":67,"update_tm":128,"read_time":142},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","Formulas/Constants: PHYS/OCEA 4411/5411 A Atmospheric Dynamics I  \n􀀀 d = 9 .8 oC/km (dry adiabatic lapse rate)  \n􀀍 = cp /cv = 1 .4  \nR = 287.05 J/(kg K)  \ncv = 717.5 J/(kg K)  \ncp = 1004.5 J/(kg K)  \ng0 = 9 .81 m/s2  \nf = 2􀀊sin􀀞  \n􀀊 = 7 .292 × 10 􀀀5 rad/sec  \n􀀚0 = 1 .225 kg/m3  \np0 = 1013 .25 hPa  \nMd = 28 .94 g/mole (Mean molecular weight of dry air)  \n􀀗 = 1 .46 × 10 􀀀5m2 /sec (sea level)  \n􀀀 d = 9 .8 oC/km  \na = 6370 km (radius of the earth)  \nspeci􀀌c volume: 􀀋 = 1/􀀚  \nRossby Number: R0 = U/fL  \nViscous Force per unit area A between two plates with relative velocity u0 and separation l:  \n􀀖Au 0  \nF = ~~ ~~  \nl  \nViscous acceleration within a 􀀍uid in the x direction due to a shear in u in the z direction (􀀗 is the kinematic viscosity):  \n􀀖 ∂2 u  ∂ 2 u  \na = = 􀀗  \n􀀚 ∂z 2 ∂z 2  \nAngular momentum: L = Iω, where the moment of inertia of a point mass m is I = mR2 (R is the distance from the axis of rotation), ω = u/R is the angular velocity, and u is the tangential (zonal)  \nvelocity.  \nMomentum/unit mass about earths axis(with zonal speed u) : M = L/m = (􀀊acos􀀞 + u)cos􀀞 Relationship between local and total derivative:  \n∂ d  \n~~ ~~ = ~~ ~~ − U · ∇  \n∂t dt  \n ∂   ∂   ∂ ∇ = i + j + k  \n∂x ∂y ∂z  \n∇2 F = F2 + 2 + 2  \nRelative vector vorticity : ω = ∇ × U  \n∂v   ∂u  \nRelative scalar vorticity : 􀀘 = −  \n∂x ∂y  \nTotal vs Local Derivative : ddt =  + U · ∇ Pressure Gradient Acceleration : Fm = − 1􀀚∇p = −∇p 􀀈 Total Gravity : g (􀀞) = g􀀃 (􀀞) + 􀀊2 R  \nDe􀀌nition of Geopotential : d􀀞 = gdz = g0 dZ  \n􀀞 (z) = Z0 z gdz  \n􀀞 (z)  \nZ = ~~ ~~  \ng0  \nHydrostatic Relationship : dpdz = −􀀚g  \ndU  1  \nMomentum Equation (Z surface) : dt = −2􀀊 × U − 􀀚 ∇p + g + Fr Primitive equations:  \ndu  uv tan􀀞   uw   1 ∂p  \ndt − a + a = − 􀀚 ∂x + 2􀀊v sin􀀞 − 2􀀊w cos􀀞 + Frx dvdt + u2~~ ~~taan􀀞 + vwa = − 1􀀚 py + −2􀀊usin􀀞 + Fry  \ndw   u2 + v 2   1 ∂p  \ndt − a = − 􀀚 ∂z − g + 2􀀊u cos􀀞 + Frz  \nIdeal Gas Law : p = 􀀚RT  \nPotential Temperature: 􀀒 = T (p0 /p)0.286 = T (p0 /p)R/cp , where p0 = 105 Pa  \nT d􀀒   dT   g   dT = + = + 􀀀 d  \n􀀒 dz dz cp dz  \nBuoyancy acceleration : B = dwdt = g ~~ ~~(T~~ ~~−T0T0~~ ~~) = g 􀀒~~ ~~0􀀒0 = −N2 􀀎z (small 􀀎z)  \n2 d ln􀀒 g d􀀒  \nBuoyancy frequency : N = g dz  = 􀀒 dz  \nN is an angular frequency so the period of the oscillation is T = 2􀀙/N  \nThickness Relationship : 􀀁Z = R~~ ~~ln (p1 /p2 )  \n 1   \nGeostrophic wind (Z surface) : Vg = k × 􀀚f ∇p  \n 1 ∂pug = − 􀀚f ∂y  \nvg = 1􀀚f px  \nApproximate Prognostic equations (coordinate form on a Z surface):  \ndu  1 ∂p  \ndt = fv − 􀀚 ∂x = f (v − vg)  \ndv   1 ∂p  \ndt = −fu − 􀀚 ∂y = −f(u − ug)  \nApproximate Prognostic equation (vector form on a Z surface):  \ndV  \n= −fk × Vag  \ndt  \nContinuity equation (Z surface) : 􀀚t + ∇ · (􀀚U) = 0  \n1 d􀀚  \nContinuity equation (Z surface) : + ∇ · U = 0  \n􀀚 dt  \nThermodynamic equation : cv dTdt + p dd􀀋t = Q˙  \nThermodynamic equation : cp dTdt − 􀀋 dpdt = Q˙  \nMechanical Energy Equation : Q˙ = ddt 􀀔 ~~ ~~(u2~~ ~~+~~ ~~v~~ ~~+~~ ~~w2~~ ~~) + 􀀈 + cvT + p􀀋􀀕 − 􀀋 pt − V · F Bernouilli Equation : (u2~~ ~~+~~ ~~v~~ ~~+~~ ~~w2~~ ~~) + 􀀈 + cvT + p􀀋 = constant  \nd􀀒   􀀒 Q˙=  \ndt T cp  \nT􀀒 􀀒z = Tz + gcp = −􀀀 + 􀀀d  \ndV  \nMomentum Equation p surface : dt + fk × V = −∇p 􀀞 De􀀌nition of pressure velocity : ω = ddpt  \n1  \nVector Geostrophic wind on pressure surface :Vg = k × f ∇p 􀀞  \nug = − ~~ ~~1f 􀀞y  \n1 ∂􀀞 vg =  \nf ∂x  \n∇p · Vg ≈ 0  \nContinuity equation in pressure coordinates : 􀀒 ux + vy􀀓 p + ωp = 0  \nContinuity equation in pressure coordinates : ∇ · Vh = − ωp  \nThermodynamic equation in pressure coordinates : 􀀒 Tt + u Tx + v Ty􀀓 − ω􀀛p = Qcp˙  \n(−∇T · Vh)  \nApproximate expression on a p surface : ω ≈ ~~ ~~  \n−􀀛p  \nApproximate expression on a PT surface : ω ≈ Vh · ∇p  \nT ∂􀀒   ∂T   RT   􀀋   ∂T   􀀀 d − 􀀀  \nStatic stability : 􀀛p = − = − + = − =  \n􀀒 ∂p ∂p cpp cp ∂p 􀀚g  \nIf pressure levels have 􀀌xed z, or ∂p/∂t = 0: ω = −􀀚gw  \nSurface Pressure Tendency : s ≈ − Z0ps (∇ · V)dp  \nKinematic Estimate of ω : ω(p) = ω(ps) − Zp 􀀒 ux + vy􀀓 dp  \nNatural coordinates : dVdt = − 􀀞s  \nV 2   ∂􀀞  \nNatural coordinates : = − − ","cbCaij7AU38x4VOX","https://ap.wps.com/l/cbCaij7AU38x4VOX","pdf",61887,"English","# Constants and thermodynamic definitions\n## Wind, forces, and momentum equations\n## Hydrostatic balance and derivatives\n## Stability, buoyancy, and thickness relations\n## Geostrophic wind, prognostic forms, and continuity\n## Pressure coordinates and thermal wind\n## Circulation and vorticity\n## Potential vorticity and vorticity tendency","[{\"question\":\"What core atmospheric constants and gas parameters are listed?\",\"answer\":\"The sheet provides values such as the dry adiabatic lapse rate, the specific heat ratio, gas constant for dry air, and standard gravity, along with Earth-rotation and sea-level reference density and pressure.\"},{\"question\":\"How are geostrophic and wind relationships expressed?\",\"answer\":\"It includes geostrophic wind relations on Z and pressure surfaces, plus approximate prognostic equations that connect ageostrophic components to pressure-gradient forcing.\"},{\"question\":\"Which stability and vertical-motion concepts are included?\",\"answer\":\"It covers potential temperature, buoyancy acceleration and buoyancy frequency, static stability, thickness relations, and links between vertical velocity and continuity in pressure coordinates.\"}]","PHYS/OCEA 4411/5411 A Atmospheric Dynamics I - Key formulas and constants | PDF",15]