Abstracts Category : Other

Modelling the Formation and Propagation of Orographic Rossby Waves

by Eskil Jonsson

Orographic Rossby waves are the main mechanism by which the jet streams meander aroundthe Earth and have possibly far-reaching impacts on weather and climate (chapter 1). Hence,they are of particular importance to study and this project should serve as a starting point inwhat to consider when trying to model these waves. For example, we have to account forpressure gradients, Coriolis effect, orography, potential vorticity conservation and also Earthscurvature at this scale. These are covered in detail in ch. 2 and adapted to the Shallow WaterEquations. In addition, some entry-level numerical techniques for solving these equations arepresented throughout ch. 2.4 and then implemented for the global-scale Shallow WaterEquations with conserved potential vorticity in ch. 3. The model is validated to work for typicalshallow water flows in a bath tub and passes common tests like the Gaussian curve test (ch.4.1). However, when considering atmospheric flows (ch. 4.2) it becomes evident that ourmodel, as well as our numerical methods are lacking and cannot reproduce Rossby waves ina stable manner. Hence, a heavily modified version of Hogans model (Hogan, n.d) isemployed with a simplified numerical scheme. With these corrections, orographic Rossbywaves appear to naturally form at appropriate locations. However, they do not fully exhibit theexpected behaviours discussed in ch. 2.2. Even Hogans model appears to have severelimitations as waves propagate in the wrong direction. Hence, this study is not complete andwarrants further development in order to be useful. Orografiska Rossby-vgor r den huvudsakliga mekanismen genom vilken jetstrmmarnaslingrar runt jorden och kan ha en omfattande inverkan p vder och klimat (kapitel 1). Drfrr de av srskild betydelse att studera och detta projekt br fungera som en utgngspunkt frvad man mste vervga nr man frsker modellera dessa vgor. Till exempel s mste vi tahnsyn till tryckgradienter, Coriolis-effekten, orografi, potentiell vorticitetsbevarande och venjordens krkning p denna skala. Dessa beskrivs i detalj i kap. 2 och anpassas tillrrelseekvationerna fr grunt vatten (Saint-Venant-ekvationerna). Drefter presenteras ngranumeriska tekniker p grundlggande niv fr att lsa dessa ekvationer i kap. 2.4, varvid desedan implementeras fr de globala Saint-Venant-ekvationerna med bevarad potentiellvorticitet i kap 3. Modellen r validerad fr typiska grunda vattenflden i ett badkar ochpasserar vanliga numeriska tester s som Gauss-kurvtestet (kap. 4.1) och bore-testet. Mennr vi vervger atmosfriska flden (kap. 4.2) blir det tydligt att vra modeller och numeriskametoder r primitiva och inte kan reproducera Rossby-vgor p ett stabilt stt. Drmed,modifierar vi Hogans modell (Hogan, n.d) fr att passa vr modell vilket resulterar orografiskaRossby-vgor. Dock s r dessa frskjutna och stmmer inte riktigt verens med teorin i kap.2.2. ven Hogans modell visar sig ha allvarliga begrnsningar d vgorna propagerar i felriktning. Drmed r denna studie