Announcements • HW5 is due at the end of today’s class period • Exam 2 is due next Wednesday (4 Nov) • Let me know if you have any conflicts or problems with this due date related to election day on 3 Nov • The exam will be posted on the class Canvas web page after Friday’s review session on 30 Oct • The exam will be a closed book exam but you will be allowed to use one double-sided cheat sheet • You should plan to complete the exam in one sitting in about 2 hours • The completed exam needs to be e-mailed to me by no later than 1:45PM on Wednesday 4 Nov • During Friday’s review session I will be happy to answer any questions about material that may be on exam 2 Balanced Flow • We will consider balanced flows in which the wind is parallel to height (pressure) contours and the horizontal momentum equation reduces to: �! �Φ + �� = − � �� • We will look at all possible force balances represented by this equation and consider when each of these balances is most appropriate. Balanced Flow: Inertial Flow • Assume negligible pressure gradient �! + �� = 0 � • What is the path followed by an air parcel for this force balance? � � = − � Antarctic Inertial Flow Balanced Flow: Cyclostrophic Flow " ! " $ • Rossby number: �� = # = #$ #% • What conditions result in a large Rossby number? • What does a large Rossby number imply about the force balance acting on the flow? �! �Φ = − � �� Balanced Flow: Cyclostrophic Flow • Can cyclostrophic flow occur around both low and high pressure centers? �Φ &.( � = −� �� Balanced Flow: Cyclostropic Flow Example: A tornado is observed to have a radius of 600 m and a wind speed of 130 m s-1 - What is the Rossby number for this flow? - Estimate the pressure at the center of this tornado, assuming that the pressure at the outer edge of the tornado is 1000 mb. Hint: Express the cyclostrophic balance in terms of pressure rather than geopotential gradient. You may assume r = 1 kg m-3 Balanced Flow: Geostrophic Wind $ • Rossby number: �� = #% • What conditions result in a small Rossby number? • What force balance is appropriate for a small Ro? �Φ �� = − �� 1 �Φ � = − ) � �� Geostrophic Wind Calculate the geostrophic wind at MPX (latitude 44.98 N) Geostrophic Wind and Divergence • Geostrophic wind in cartesian coordinates: 1 �Φ 1 �Φ � = − �⃑ + �⃑ " � �� � �� • Neglecting variations in f the geostrophic wind is non-divergent ��) ��) ∇ . � = + = 0 ) �� �� Balanced Flow: Gradient Wind • What force balance do we need to consider if Ro ~1 and the pressure gradient cannot be neglected? �! �Φ + �� = − � �� • The solution of this quadratic equation gives the gradient wind: ".$ �� �!�! �Φ � = − ± − � 2 4 �� Balanced Flow: Gradient Wind Regular low Regular high • There are 4 physically reasonable solutions for the gradient wind • Regular low (R>0) ".$ �� �!�! �Φ � = − + − � 2 4 �� Anomalous low Anomalous high • Regular high (R<0) ".$ �� �!�! �Φ � = − − − � 2 4 �� Gradient Wind Calculate the geostrophic and gradient wind at REV and RAP How do we estimate the radius of curvature? Gradient Wind Calculate the geostrophic and gradient wind at REV and RAP REV Dn = 320 km |R| = 420 km f = 39.51 N RAP Dn = 302 km |R| = 1121 km f = 44.15 N Balanced Flow: Gradient Wind • How does the gradient wind compare to the geostrophic wind at REV (RAP)? • Under what conditions is Vgrad > Vgeo (Vgrad > Vgeo)? • What is the physical explanation for this? Regular low Regular high Ageostrophic Flow • The ageostrophic wind (Va) is the given by the difference between the actual wind (V) and the geostrophic wind (Vg) �* = � − �) or � = �) + �* • Since the gradient wind is the best balanced flow estimate of the wind we will assume that the actual wind is given by the gradient wind Ageostrophic Flow and Divergence What is the direction of the ageostrophic wind at REV (RAP)? What does this suggest about where divergence (convergence) occurs relative to troughs and ridges? Ageostrophic Flow and Divergence • In troughs: • The actual (and gradient) wind is less than geostrophic • The ageostrophic wind is directed opposite the geostrophic wind • In ridges: • The actual (and gradient) wind is greater than geostrophic • The ageostrophic wind is directed in the same direction as the geostrophic wind • This causes divergence to occur downstream of troughs and convergence to occur downstream of ridges Gradient Wind: Limit for H Pressure • For flow around high pressure we found there was a limit on how large the pressure gradient could become • What is the physical reason for this limit?.